stochastic

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stochastic

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Extension repository on GitHub

Extension descriptor (YAML)

Add comprehensive statistical distribution functions to DuckDB, enabling advanced statistical analysis, probability calculations, and random sampling directly within SQL queries.

Maintainer(s): rustyconover

Installing and Loading

INSTALL stochastic FROM community;
LOAD stochastic;

About stochastic

For more information regarding usage, see the documentation.

Added Functions

function_name	function_type	description	comment	examples
dist_bernoulli_cdf	scalar	Computes the cumulative distribution function (CDF) of the bernoulli distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_bernoulli_cdf(0.5, 0)]
dist_bernoulli_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the bernoulli distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_bernoulli_cdf_complement(0.5, 0)]
dist_bernoulli_chf	scalar	Computes the cumulative hazard function of the bernoulli distribution.	NULL	[dist_bernoulli_chf(0.5, 0)]
dist_bernoulli_hazard	scalar	Computes the hazard function of the bernoulli distribution.	NULL	[dist_bernoulli_hazard(0.5, 0)]
dist_bernoulli_kurtosis	scalar	Returns the kurtosis of the bernoulli distribution.	NULL	[dist_bernoulli_kurtosis(0.5)]
dist_bernoulli_kurtosis_excess	scalar	Returns the excess kurtosis of the bernoulli distribution.	NULL	[dist_bernoulli_kurtosis_excess(0.5)]
dist_bernoulli_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the bernoulli distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_bernoulli_log_cdf(0.5, 0)]
dist_bernoulli_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the bernoulli distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_bernoulli_log_cdf_complement(0.5, 0)]
dist_bernoulli_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the bernoulli distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_bernoulli_log_pdf(0.5, 1)]
dist_bernoulli_mean	scalar	Returns the mean (μ) of the bernoulli distribution, which is the first moment.	NULL	[dist_bernoulli_mean(0.5)]
dist_bernoulli_median	scalar	Returns the median (50th percentile) of the bernoulli distribution, which equals the mean.	NULL	[dist_bernoulli_median(0.5)]
dist_bernoulli_mode	scalar	Returns the mode (most likely value) of the bernoulli distribution, which equals the mean.	NULL	[dist_bernoulli_mode(0.5)]
dist_bernoulli_pdf	scalar	Computes the probability density function (PDF) of the bernoulli distribution. Returns the probability densityat point x for a bernoulli distribution with specified parameters.	NULL	[dist_bernoulli_pdf(0.5, 1)]
dist_bernoulli_quantile	scalar	Computes the quantile function (inverse CDF) of the bernoulli distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_bernoulli_quantile(0.5, 0.95)]
dist_bernoulli_quantile_complement	scalar	Computes the complementary quantile function of the bernoulli distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_bernoulli_quantile_complement(0.5, 0.05)]
dist_bernoulli_range	scalar	Returns the range of the bernoulli distribution.	NULL	[dist_bernoulli_range(0.5)]
dist_bernoulli_sample	scalar	Generates random samples from the bernoulli distribution with specified parameters.	NULL	[dist_bernoulli_sample(0.5)]
dist_bernoulli_skewness	scalar	Returns the skewness of the bernoulli distribution.	NULL	[dist_bernoulli_skewness(0.5)]
dist_bernoulli_stddev	scalar	Returns the standard deviation (σ) of the bernoulli distribution.	NULL	[dist_bernoulli_stddev(0.5)]
dist_bernoulli_support	scalar	Returns the support of the bernoulli distribution.	NULL	[dist_bernoulli_support(0.5)]
dist_bernoulli_variance	scalar	Returns the variance (σ²) of the bernoulli distribution.	NULL	[dist_bernoulli_variance(0.5)]
dist_beta_cdf	scalar	Computes the cumulative distribution function (CDF) of the beta distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_beta_cdf(2.0, 5.0, 0.5)]
dist_beta_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the beta distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_beta_cdf_complement(2.0, 5.0, 0.5)]
dist_beta_chf	scalar	Computes the cumulative hazard function of the beta distribution.	NULL	[dist_beta_chf(2.0, 5.0, 0.5)]
dist_beta_hazard	scalar	Computes the hazard function of the beta distribution.	NULL	[dist_beta_hazard(2.0, 5.0, 0.5)]
dist_beta_kurtosis	scalar	Returns the kurtosis of the beta distribution.	NULL	[dist_beta_kurtosis(2.0, 5.0)]
dist_beta_kurtosis_excess	scalar	Returns the excess kurtosis of the beta distribution.	NULL	[dist_beta_kurtosis_excess(2.0, 5.0)]
dist_beta_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the beta distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_beta_log_cdf(2.0, 5.0, 0.5)]
dist_beta_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the beta distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_beta_log_cdf_complement(2.0, 5.0, 0.5)]
dist_beta_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the beta distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_beta_log_pdf(2.0, 5.0, 0.5)]
dist_beta_mean	scalar	Returns the mean (μ) of the beta distribution, which is the first moment.	NULL	[dist_beta_mean(2.0, 5.0)]
dist_beta_median	scalar	Returns the median (50th percentile) of the beta distribution, which equals the mean.	NULL	[dist_beta_median(2.0, 5.0)]
dist_beta_mode	scalar	Returns the mode (most likely value) of the beta distribution, which equals the mean.	NULL	[dist_beta_mode(2.0, 5.0)]
dist_beta_pdf	scalar	Computes the probability density function (PDF) of the beta distribution. Returns the probability densityat point x for a beta distribution with specified parameters.	NULL	[dist_beta_pdf(2.0, 5.0, 0.5)]
dist_beta_quantile	scalar	Computes the quantile function (inverse CDF) of the beta distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_beta_quantile(2.0, 5.0, 0.95)]
dist_beta_quantile_complement	scalar	Computes the complementary quantile function of the beta distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_beta_quantile_complement(2.0, 5.0, 0.05)]
dist_beta_range	scalar	Returns the range of the beta distribution.	NULL	[dist_beta_range(2.0, 5.0)]
dist_beta_sample	scalar	Generates random samples from the beta distribution with specified parameters.	NULL	[dist_beta_sample(2.0, 5.0)]
dist_beta_skewness	scalar	Returns the skewness of the beta distribution.	NULL	[dist_beta_skewness(2.0, 5.0)]
dist_beta_stddev	scalar	Returns the standard deviation (σ) of the beta distribution.	NULL	[dist_beta_stddev(2.0, 5.0)]
dist_beta_support	scalar	Returns the support of the beta distribution.	NULL	[dist_beta_support(2.0, 5.0)]
dist_beta_variance	scalar	Returns the variance (σ²) of the beta distribution.	NULL	[dist_beta_variance(2.0, 5.0)]
dist_binomial_cdf	scalar	Computes the cumulative distribution function (CDF) of the binomial distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_binomial_cdf(10, 0.5, 5)]
dist_binomial_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the binomial distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_binomial_cdf_complement(10, 0.5, 5)]
dist_binomial_chf	scalar	Computes the cumulative hazard function of the binomial distribution.	NULL	[dist_binomial_chf(10, 0.5, 5)]
dist_binomial_hazard	scalar	Computes the hazard function of the binomial distribution.	NULL	[dist_binomial_hazard(10, 0.5, 5)]
dist_binomial_kurtosis	scalar	Returns the kurtosis of the binomial distribution.	NULL	[dist_binomial_kurtosis(10, 0.5)]
dist_binomial_kurtosis_excess	scalar	Returns the excess kurtosis of the binomial distribution.	NULL	[dist_binomial_kurtosis_excess(10, 0.5)]
dist_binomial_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the binomial distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_binomial_log_cdf(10, 0.5, 5)]
dist_binomial_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the binomial distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_binomial_log_cdf_complement(10, 0.5, 5)]
dist_binomial_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the binomial distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_binomial_log_pdf(10, 0.5, 5)]
dist_binomial_median	scalar	Returns the median (50th percentile) of the binomial distribution, which equals the mean.	NULL	[dist_binomial_median(10, 0.5)]
dist_binomial_mode	scalar	Returns the mode (most likely value) of the binomial distribution, which equals the mean.	NULL	[dist_binomial_mode(10, 0.5)]
dist_binomial_pdf	scalar	Computes the probability density function (PDF) of the binomial distribution. Returns the probability densityat point x for a binomial distribution with specified parameters.	NULL	[dist_binomial_pdf(10, 0.5, 5)]
dist_binomial_quantile	scalar	Computes the quantile function (inverse CDF) of the binomial distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_binomial_quantile(10, 0.5, 0.95)]
dist_binomial_quantile_complement	scalar	Computes the complementary quantile function of the binomial distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_binomial_quantile_complement(10, 0.5, 0.05)]
dist_binomial_range	scalar	Returns the range of the binomial distribution.	NULL	[dist_binomial_range(10, 0.5)]
dist_binomial_sample	scalar	Generates random samples from the binomial distribution with specified parameters.	NULL	[dist_binomial_sample(10, 0.5)]
dist_binomial_skewness	scalar	Returns the skewness of the binomial distribution.	NULL	[dist_binomial_skewness(10, 0.5)]
dist_binomial_support	scalar	Returns the support of the binomial distribution.	NULL	[dist_binomial_support(10, 0.5)]
dist_binomial_variance	scalar	Returns the variance (σ²) of the binomial distribution.	NULL	[dist_binomial_variance(10, 0.5)]
dist_chi_squared_cdf	scalar	Computes the cumulative distribution function (CDF) of the chi_squared distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_chi_squared_cdf(5, 3.0)]
dist_chi_squared_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the chi_squared distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_chi_squared_cdf_complement(5, 3.0)]
dist_chi_squared_chf	scalar	Computes the cumulative hazard function of the chi_squared distribution.	NULL	[dist_chi_squared_chf(5, 3.0)]
dist_chi_squared_hazard	scalar	Computes the hazard function of the chi_squared distribution.	NULL	[dist_chi_squared_hazard(5, 3.0)]
dist_chi_squared_kurtosis	scalar	Returns the kurtosis of the chi_squared distribution.	NULL	[dist_chi_squared_kurtosis(5)]
dist_chi_squared_kurtosis_excess	scalar	Returns the excess kurtosis of the chi_squared distribution.	NULL	[dist_chi_squared_kurtosis_excess(5)]
dist_chi_squared_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the chi_squared distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_chi_squared_log_cdf(5, 3.0)]
dist_chi_squared_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the chi_squared distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_chi_squared_log_cdf_complement(5, 3.0)]
dist_chi_squared_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the chi_squared distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_chi_squared_log_pdf(5, 3.0)]
dist_chi_squared_mean	scalar	Returns the mean (μ) of the chi_squared distribution, which is the first moment.	NULL	[dist_chi_squared_mean(5)]
dist_chi_squared_median	scalar	Returns the median (50th percentile) of the chi_squared distribution, which equals the mean.	NULL	[dist_chi_squared_median(5)]
dist_chi_squared_mode	scalar	Returns the mode (most likely value) of the chi_squared distribution, which equals the mean.	NULL	[dist_chi_squared_mode(5)]
dist_chi_squared_pdf	scalar	Computes the probability density function (PDF) of the chi_squared distribution. Returns the probability densityat point x for a chi_squared distribution with specified parameters.	NULL	[dist_chi_squared_pdf(5, 3.0)]
dist_chi_squared_quantile	scalar	Computes the quantile function (inverse CDF) of the chi_squared distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_chi_squared_quantile(5, 0.95)]
dist_chi_squared_quantile_complement	scalar	Computes the complementary quantile function of the chi_squared distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_chi_squared_quantile_complement(5, 0.05)]
dist_chi_squared_range	scalar	Returns the range of the chi_squared distribution.	NULL	[dist_chi_squared_range(5)]
dist_chi_squared_sample	scalar	Generates random samples from the chi_squared distribution with specified parameters.	NULL	[dist_chi_squared_sample(5)]
dist_chi_squared_skewness	scalar	Returns the skewness of the chi_squared distribution.	NULL	[dist_chi_squared_skewness(5)]
dist_chi_squared_stddev	scalar	Returns the standard deviation (σ) of the chi_squared distribution.	NULL	[dist_chi_squared_stddev(5)]
dist_chi_squared_support	scalar	Returns the support of the chi_squared distribution.	NULL	[dist_chi_squared_support(5)]
dist_chi_squared_variance	scalar	Returns the variance (σ²) of the chi_squared distribution.	NULL	[dist_chi_squared_variance(5)]
dist_exponential_cdf	scalar	Computes the cumulative distribution function (CDF) of the exponential distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_exponential_cdf(1.0, 0.5)]
dist_exponential_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the exponential distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_exponential_cdf_complement(1.0, 0.5)]
dist_exponential_chf	scalar	Computes the cumulative hazard function of the exponential distribution.	NULL	[dist_exponential_chf(1.0, 0.5)]
dist_exponential_hazard	scalar	Computes the hazard function of the exponential distribution.	NULL	[dist_exponential_hazard(1.0, 0.5)]
dist_exponential_kurtosis	scalar	Returns the kurtosis of the exponential distribution.	NULL	[dist_exponential_kurtosis(1.0)]
dist_exponential_kurtosis_excess	scalar	Returns the excess kurtosis of the exponential distribution.	NULL	[dist_exponential_kurtosis_excess(1.0)]
dist_exponential_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the exponential distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_exponential_log_cdf(1.0, 0.5)]
dist_exponential_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the exponential distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_exponential_log_cdf_complement(1.0, 0.5)]
dist_exponential_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the exponential distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_exponential_log_pdf(1.0, 0.5)]
dist_exponential_mean	scalar	Returns the mean (μ) of the exponential distribution, which is the first moment.	NULL	[dist_exponential_mean(1.0)]
dist_exponential_median	scalar	Returns the median (50th percentile) of the exponential distribution, which equals the mean.	NULL	[dist_exponential_median(1.0)]
dist_exponential_mode	scalar	Returns the mode (most likely value) of the exponential distribution, which equals the mean.	NULL	[dist_exponential_mode(1.0)]
dist_exponential_pdf	scalar	Computes the probability density function (PDF) of the exponential distribution. Returns the probability densityat point x for a exponential distribution with specified parameters.	NULL	[dist_exponential_pdf(1.0, 0.5)]
dist_exponential_quantile	scalar	Computes the quantile function (inverse CDF) of the exponential distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_exponential_quantile(1.0, 0.95)]
dist_exponential_quantile_complement	scalar	Computes the complementary quantile function of the exponential distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_exponential_quantile_complement(1.0, 0.05)]
dist_exponential_range	scalar	Returns the range of the exponential distribution.	NULL	[dist_exponential_range(1.0)]
dist_exponential_sample	scalar	Generates random samples from the exponential distribution with specified parameters.	NULL	[dist_exponential_sample(1.0)]
dist_exponential_skewness	scalar	Returns the skewness of the exponential distribution.	NULL	[dist_exponential_skewness(1.0)]
dist_exponential_stddev	scalar	Returns the standard deviation (σ) of the exponential distribution.	NULL	[dist_exponential_stddev(1.0)]
dist_exponential_support	scalar	Returns the support of the exponential distribution.	NULL	[dist_exponential_support(1.0)]
dist_exponential_variance	scalar	Returns the variance (σ²) of the exponential distribution.	NULL	[dist_exponential_variance(1.0)]
dist_extreme_value_cdf	scalar	Computes the cumulative distribution function (CDF) of the extreme_value distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_extreme_value_cdf(0, 1.0, 0.5)]
dist_extreme_value_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the extreme_value distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_extreme_value_cdf_complement(0, 1.0, 0.5)]
dist_extreme_value_chf	scalar	Computes the cumulative hazard function of the extreme_value distribution.	NULL	[dist_extreme_value_chf(0, 1.0, 0.5)]
dist_extreme_value_hazard	scalar	Computes the hazard function of the extreme_value distribution.	NULL	[dist_extreme_value_hazard(0, 1.0, 0.5)]
dist_extreme_value_kurtosis	scalar	Returns the kurtosis of the extreme_value distribution.	NULL	[dist_extreme_value_kurtosis(0.0, 1.0)]
dist_extreme_value_kurtosis_excess	scalar	Returns the excess kurtosis of the extreme_value distribution.	NULL	[dist_extreme_value_kurtosis_excess(0.0, 1.0)]
dist_extreme_value_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the extreme_value distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_extreme_value_log_cdf(0, 1.0, 0.5)]
dist_extreme_value_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the extreme_value distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_extreme_value_log_cdf_complement(0, 1.0, 0.5)]
dist_extreme_value_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the extreme_value distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_extreme_value_log_pdf(0, 1.0, 0.5)]
dist_extreme_value_median	scalar	Returns the median (50th percentile) of the extreme_value distribution, which equals the mean.	NULL	[dist_extreme_value_median(0.0, 1.0)]
dist_extreme_value_mode	scalar	Returns the mode (most likely value) of the extreme_value distribution, which equals the mean.	NULL	[dist_extreme_value_mode(0.0, 1.0)]
dist_extreme_value_pdf	scalar	Computes the probability density function (PDF) of the extreme_value distribution. Returns the probability densityat point x for a extreme_value distribution with specified parameters.	NULL	[dist_extreme_value_pdf(0, 1.0, 0.5)]
dist_extreme_value_quantile	scalar	Computes the quantile function (inverse CDF) of the extreme_value distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_extreme_value_quantile(0, 1.0, 0.95)]
dist_extreme_value_quantile_complement	scalar	Computes the complementary quantile function of the extreme_value distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_extreme_value_quantile_complement(0, 1.0, 0.95)]
dist_extreme_value_range	scalar	Returns the range of the extreme_value distribution.	NULL	[dist_extreme_value_range(0.0, 1.0)]
dist_extreme_value_sample	scalar	Generates random samples from the extreme_value distribution with specified parameters.	NULL	[dist_extreme_value_sample(0.0, 1.0)]
dist_extreme_value_skewness	scalar	Returns the skewness of the extreme_value distribution.	NULL	[dist_extreme_value_skewness(0.0, 1.0)]
dist_extreme_value_support	scalar	Returns the support of the extreme_value distribution.	NULL	[dist_extreme_value_support(0.0, 1.0)]
dist_extreme_value_variance	scalar	Returns the variance (σ²) of the extreme_value distribution.	NULL	[dist_extreme_value_variance(0.0, 1.0)]
dist_fisher_f_cdf	scalar	Computes the cumulative distribution function (CDF) of the fisher_f distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_fisher_f_cdf(5, 10, 0.5)]
dist_fisher_f_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the fisher_f distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_fisher_f_cdf_complement(5, 10, 0.5)]
dist_fisher_f_chf	scalar	Computes the cumulative hazard function of the fisher_f distribution.	NULL	[dist_fisher_f_chf(5, 10, 0.5)]
dist_fisher_f_hazard	scalar	Computes the hazard function of the fisher_f distribution.	NULL	[dist_fisher_f_hazard(5, 10, 0.5)]
dist_fisher_f_kurtosis	scalar	Returns the kurtosis of the fisher_f distribution.	NULL	[dist_fisher_f_kurtosis(5, 10)]
dist_fisher_f_kurtosis_excess	scalar	Returns the excess kurtosis of the fisher_f distribution.	NULL	[dist_fisher_f_kurtosis_excess(5, 10)]
dist_fisher_f_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the fisher_f distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_fisher_f_log_cdf(5, 10, 0.5)]
dist_fisher_f_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the fisher_f distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_fisher_f_log_cdf_complement(5, 10, 0.5)]
dist_fisher_f_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the fisher_f distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_fisher_f_log_pdf(5, 10, 0.5)]
dist_fisher_f_median	scalar	Returns the median (50th percentile) of the fisher_f distribution, which equals the mean.	NULL	[dist_fisher_f_median(5, 10)]
dist_fisher_f_mode	scalar	Returns the mode (most likely value) of the fisher_f distribution, which equals the mean.	NULL	[dist_fisher_f_mode(5, 10)]
dist_fisher_f_pdf	scalar	Computes the probability density function (PDF) of the fisher_f distribution. Returns the probability densityat point x for a fisher_f distribution with specified parameters.	NULL	[dist_fisher_f_pdf(5, 10, 0.5)]
dist_fisher_f_quantile	scalar	Computes the quantile function (inverse CDF) of the fisher_f distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_fisher_f_quantile(5, 10, 0.95)]
dist_fisher_f_quantile_complement	scalar	Computes the complementary quantile function of the fisher_f distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_fisher_f_quantile_complement(5, 10, 0.05)]
dist_fisher_f_range	scalar	Returns the range of the fisher_f distribution.	NULL	[dist_fisher_f_range(5, 10)]
dist_fisher_f_sample	scalar	Generates random samples from the fisher_f distribution with specified parameters.	NULL	[dist_fisher_f_sample(5, 10)]
dist_fisher_f_skewness	scalar	Returns the skewness of the fisher_f distribution.	NULL	[dist_fisher_f_skewness(5, 10)]
dist_fisher_f_support	scalar	Returns the support of the fisher_f distribution.	NULL	[dist_fisher_f_support(5, 10)]
dist_fisher_f_variance	scalar	Returns the variance (σ²) of the fisher_f distribution.	NULL	[dist_fisher_f_variance(5, 10)]
dist_gamma_cdf	scalar	Computes the cumulative distribution function (CDF) of the gamma distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_gamma_cdf(2.0, 1.0, 1.5)]
dist_gamma_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the gamma distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_gamma_cdf_complement(2.0, 1.0, 1.5)]
dist_gamma_chf	scalar	Computes the cumulative hazard function of the gamma distribution.	NULL	[dist_gamma_chf(2.0, 1.0, 1.5)]
dist_gamma_hazard	scalar	Computes the hazard function of the gamma distribution.	NULL	[dist_gamma_hazard(2.0, 1.0, 1.5)]
dist_gamma_kurtosis	scalar	Returns the kurtosis of the gamma distribution.	NULL	[dist_gamma_kurtosis(2.0, 1.0)]
dist_gamma_kurtosis_excess	scalar	Returns the excess kurtosis of the gamma distribution.	NULL	[dist_gamma_kurtosis_excess(2.0, 1.0)]
dist_gamma_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the gamma distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_gamma_log_cdf(2.0, 1.0, 1.5)]
dist_gamma_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the gamma distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_gamma_log_cdf_complement(2.0, 1.0, 1.5)]
dist_gamma_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the gamma distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_gamma_log_pdf(2.0, 1.0, 1.5)]
dist_gamma_mean	scalar	Returns the mean (μ) of the gamma distribution, which is the first moment.	NULL	[dist_gamma_mean(2.0, 1.0)]
dist_gamma_median	scalar	Returns the median (50th percentile) of the gamma distribution, which equals the mean.	NULL	[dist_gamma_median(2.0, 1.0)]
dist_gamma_mode	scalar	Returns the mode (most likely value) of the gamma distribution, which equals the mean.	NULL	[dist_gamma_mode(2.0, 1.0)]
dist_gamma_pdf	scalar	Computes the probability density function (PDF) of the gamma distribution. Returns the probability densityat point x for a gamma distribution with specified parameters.	NULL	[dist_gamma_pdf(2.0, 1.0, 1.5)]
dist_gamma_quantile	scalar	Computes the quantile function (inverse CDF) of the gamma distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_gamma_quantile(2.0, 1.0, 0.95)]
dist_gamma_quantile_complement	scalar	Computes the complementary quantile function of the gamma distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_gamma_quantile_complement(2.0, 1.0, 0.05)]
dist_gamma_range	scalar	Returns the range of the gamma distribution.	NULL	[dist_gamma_range(2.0, 1.0)]
dist_gamma_sample	scalar	Generates random samples from the gamma distribution with specified parameters.	NULL	[dist_gamma_sample(2.0, 1.0)]
dist_gamma_skewness	scalar	Returns the skewness of the gamma distribution.	NULL	[dist_gamma_skewness(2.0, 1.0)]
dist_gamma_stddev	scalar	Returns the standard deviation (σ) of the gamma distribution.	NULL	[dist_gamma_stddev(2.0, 1.0)]
dist_gamma_support	scalar	Returns the support of the gamma distribution.	NULL	[dist_gamma_support(2.0, 1.0)]
dist_gamma_variance	scalar	Returns the variance (σ²) of the gamma distribution.	NULL	[dist_gamma_variance(2.0, 1.0)]
dist_geometric_cdf	scalar	Computes the cumulative distribution function (CDF) of the geometric distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_geometric_cdf(0.5, 2)]
dist_geometric_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the geometric distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_geometric_cdf_complement(0.5, 2)]
dist_geometric_chf	scalar	Computes the cumulative hazard function of the geometric distribution.	NULL	[dist_geometric_chf(0.5, 2)]
dist_geometric_hazard	scalar	Computes the hazard function of the geometric distribution.	NULL	[dist_geometric_hazard(0.5, 2)]
dist_geometric_kurtosis	scalar	Returns the kurtosis of the geometric distribution.	NULL	[dist_geometric_kurtosis(0.5)]
dist_geometric_kurtosis_excess	scalar	Returns the excess kurtosis of the geometric distribution.	NULL	[dist_geometric_kurtosis_excess(0.5)]
dist_geometric_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the geometric distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_geometric_log_cdf(0.5, 2)]
dist_geometric_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the geometric distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_geometric_log_cdf_complement(0.5, 2)]
dist_geometric_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the geometric distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_geometric_log_pdf(0.5, 2)]
dist_geometric_mean	scalar	Returns the mean (μ) of the geometric distribution, which is the first moment.	NULL	[dist_geometric_mean(0.5)]
dist_geometric_median	scalar	Returns the median (50th percentile) of the geometric distribution, which equals the mean.	NULL	[dist_geometric_median(0.5)]
dist_geometric_mode	scalar	Returns the mode (most likely value) of the geometric distribution, which equals the mean.	NULL	[dist_geometric_mode(0.5)]
dist_geometric_pdf	scalar	Computes the probability density function (PDF) of the geometric distribution. Returns the probability densityat point x for a geometric distribution with specified parameters.	NULL	[dist_geometric_pdf(0.5, 2)]
dist_geometric_quantile	scalar	Computes the quantile function (inverse CDF) of the geometric distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_geometric_quantile(0.5, 0.95)]
dist_geometric_quantile_complement	scalar	Computes the complementary quantile function of the geometric distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_geometric_quantile_complement(0.5, 0.05)]
dist_geometric_range	scalar	Returns the range of the geometric distribution.	NULL	[dist_geometric_range(0.5)]
dist_geometric_sample	scalar	Generates random samples from the geometric distribution with specified parameters.	NULL	[dist_geometric_sample(0.5)]
dist_geometric_skewness	scalar	Returns the skewness of the geometric distribution.	NULL	[dist_geometric_skewness(0.5)]
dist_geometric_stddev	scalar	Returns the standard deviation (σ) of the geometric distribution.	NULL	[dist_geometric_stddev(0.5)]
dist_geometric_support	scalar	Returns the support of the geometric distribution.	NULL	[dist_geometric_support(0.5)]
dist_geometric_variance	scalar	Returns the variance (σ²) of the geometric distribution.	NULL	[dist_geometric_variance(0.5)]
dist_laplace_cdf	scalar	Computes the cumulative distribution function (CDF) of the laplace distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_laplace_cdf(0, 1.0, 0.5)]
dist_laplace_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the laplace distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_laplace_cdf_complement(0, 1.0, 0.5)]
dist_laplace_chf	scalar	Computes the cumulative hazard function of the laplace distribution.	NULL	[dist_laplace_chf(0, 1.0, 0.5)]
dist_laplace_hazard	scalar	Computes the hazard function of the laplace distribution.	NULL	[dist_laplace_hazard(0, 1.0, 0.5)]
dist_laplace_kurtosis	scalar	Returns the kurtosis of the laplace distribution.	NULL	[dist_laplace_kurtosis(0.0, 1.0)]
dist_laplace_kurtosis_excess	scalar	Returns the excess kurtosis of the laplace distribution.	NULL	[dist_laplace_kurtosis_excess(0.0, 1.0)]
dist_laplace_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the laplace distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_laplace_log_cdf(0, 1.0, 0.5)]
dist_laplace_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the laplace distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_laplace_log_cdf_complement(0, 1.0, 0.5)]
dist_laplace_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the laplace distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_laplace_log_pdf(0, 1.0, 0.5)]
dist_laplace_mean	scalar	Returns the mean (μ) of the laplace distribution, which is the first moment.	NULL	[dist_laplace_mean(0.0, 1.0)]
dist_laplace_median	scalar	Returns the median (50th percentile) of the laplace distribution, which equals the mean.	NULL	[dist_laplace_median(0.0, 1.0)]
dist_laplace_mode	scalar	Returns the mode (most likely value) of the laplace distribution, which equals the mean.	NULL	[dist_laplace_mode(0.0, 1.0)]
dist_laplace_pdf	scalar	Computes the probability density function (PDF) of the laplace distribution. Returns the probability densityat point x for a laplace distribution with specified parameters.	NULL	[dist_laplace_pdf(0, 1.0, 0.5)]
dist_laplace_quantile	scalar	Computes the quantile function (inverse CDF) of the laplace distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_laplace_quantile(0, 1.0, 0.95)]
dist_laplace_quantile_complement	scalar	Computes the complementary quantile function of the laplace distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_laplace_quantile_complement(0, 1.0, 0.95)]
dist_laplace_range	scalar	Returns the range of the laplace distribution.	NULL	[dist_laplace_range(0.0, 1.0)]
dist_laplace_sample	scalar	Generates random samples from the laplace distribution with specified parameters.	NULL	[dist_laplace_sample(0.0, 1.0)]
dist_laplace_skewness	scalar	Returns the skewness of the laplace distribution.	NULL	[dist_laplace_skewness(0.0, 1.0)]
dist_laplace_stddev	scalar	Returns the standard deviation (σ) of the laplace distribution.	NULL	[dist_laplace_stddev(0.0, 1.0)]
dist_laplace_support	scalar	Returns the support of the laplace distribution.	NULL	[dist_laplace_support(0.0, 1.0)]
dist_laplace_variance	scalar	Returns the variance (σ²) of the laplace distribution.	NULL	[dist_laplace_variance(0.0, 1.0)]
dist_logistic_cdf	scalar	Computes the cumulative distribution function (CDF) of the logistic distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_logistic_cdf(0, 1.0, 0.5)]
dist_logistic_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the logistic distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_logistic_cdf_complement(0, 1.0, 0.5)]
dist_logistic_chf	scalar	Computes the cumulative hazard function of the logistic distribution.	NULL	[dist_logistic_chf(0, 1.0, 0.5)]
dist_logistic_hazard	scalar	Computes the hazard function of the logistic distribution.	NULL	[dist_logistic_hazard(0, 1.0, 0.5)]
dist_logistic_kurtosis	scalar	Returns the kurtosis of the logistic distribution.	NULL	[dist_logistic_kurtosis(0.0, 1.0)]
dist_logistic_kurtosis_excess	scalar	Returns the excess kurtosis of the logistic distribution.	NULL	[dist_logistic_kurtosis_excess(0.0, 1.0)]
dist_logistic_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the logistic distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_logistic_log_cdf(0, 1.0, 0.5)]
dist_logistic_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the logistic distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_logistic_log_cdf_complement(0, 1.0, 0.5)]
dist_logistic_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the logistic distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_logistic_log_pdf(0, 1.0, 0.5)]
dist_logistic_median	scalar	Returns the median (50th percentile) of the logistic distribution, which equals the mean.	NULL	[dist_logistic_median(0.0, 1.0)]
dist_logistic_mode	scalar	Returns the mode (most likely value) of the logistic distribution, which equals the mean.	NULL	[dist_logistic_mode(0.0, 1.0)]
dist_logistic_pdf	scalar	Computes the probability density function (PDF) of the logistic distribution. Returns the probability densityat point x for a logistic distribution with specified parameters.	NULL	[dist_logistic_pdf(0, 1.0, 0.5)]
dist_logistic_quantile	scalar	Computes the quantile function (inverse CDF) of the logistic distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_logistic_quantile(0, 1.0, 0.95)]
dist_logistic_quantile_complement	scalar	Computes the complementary quantile function of the logistic distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_logistic_quantile_complement(0, 1.0, 0.95)]
dist_logistic_range	scalar	Returns the range of the logistic distribution.	NULL	[dist_logistic_range(0.0, 1.0)]
dist_logistic_skewness	scalar	Returns the skewness of the logistic distribution.	NULL	[dist_logistic_skewness(0.0, 1.0)]
dist_logistic_support	scalar	Returns the support of the logistic distribution.	NULL	[dist_logistic_support(0.0, 1.0)]
dist_logistic_variance	scalar	Returns the variance (σ²) of the logistic distribution.	NULL	[dist_logistic_variance(0.0, 1.0)]
dist_lognormal_cdf	scalar	Computes the cumulative distribution function (CDF) of the lognormal distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_lognormal_cdf(0, 1.0, 0.5)]
dist_lognormal_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the lognormal distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_lognormal_cdf_complement(0, 1.0, 0.5)]
dist_lognormal_chf	scalar	Computes the cumulative hazard function of the lognormal distribution.	NULL	[dist_lognormal_chf(0, 1.0, 0.5)]
dist_lognormal_hazard	scalar	Computes the hazard function of the lognormal distribution.	NULL	[dist_lognormal_hazard(0, 1.0, 0.5)]
dist_lognormal_kurtosis	scalar	Returns the kurtosis of the lognormal distribution.	NULL	[dist_lognormal_kurtosis(0.0, 1.0)]
dist_lognormal_kurtosis_excess	scalar	Returns the excess kurtosis of the lognormal distribution.	NULL	[dist_lognormal_kurtosis_excess(0.0, 1.0)]
dist_lognormal_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the lognormal distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_lognormal_log_cdf(0, 1.0, 0.5)]
dist_lognormal_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the lognormal distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_lognormal_log_cdf_complement(0, 1.0, 0.5)]
dist_lognormal_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the lognormal distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_lognormal_log_pdf(0, 1.0, 0.5)]
dist_lognormal_mean	scalar	Returns the mean (μ) of the lognormal distribution, which is the first moment.	NULL	[dist_lognormal_mean(0.0, 1.0)]
dist_lognormal_median	scalar	Returns the median (50th percentile) of the lognormal distribution, which equals the mean.	NULL	[dist_lognormal_median(0.0, 1.0)]
dist_lognormal_mode	scalar	Returns the mode (most likely value) of the lognormal distribution, which equals the mean.	NULL	[dist_lognormal_mode(0.0, 1.0)]
dist_lognormal_pdf	scalar	Computes the probability density function (PDF) of the lognormal distribution. Returns the probability densityat point x for a lognormal distribution with specified parameters.	NULL	[dist_lognormal_pdf(0, 1.0, 0.5)]
dist_lognormal_quantile	scalar	Computes the quantile function (inverse CDF) of the lognormal distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_lognormal_quantile(0, 1.0, 0.95)]
dist_lognormal_quantile_complement	scalar	Computes the complementary quantile function of the lognormal distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_lognormal_quantile_complement(0, 1.0, 0.95)]
dist_lognormal_range	scalar	Returns the range of the lognormal distribution.	NULL	[dist_lognormal_range(0.0, 1.0)]
dist_lognormal_sample	scalar	Generates random samples from the lognormal distribution with specified parameters.	NULL	[dist_lognormal_sample(0.0, 1.0)]
dist_lognormal_skewness	scalar	Returns the skewness of the lognormal distribution.	NULL	[dist_lognormal_skewness(0.0, 1.0)]
dist_lognormal_stddev	scalar	Returns the standard deviation (σ) of the lognormal distribution.	NULL	[dist_lognormal_stddev(0.0, 1.0)]
dist_lognormal_support	scalar	Returns the support of the lognormal distribution.	NULL	[dist_lognormal_support(0.0, 1.0)]
dist_lognormal_variance	scalar	Returns the variance (σ²) of the lognormal distribution.	NULL	[dist_lognormal_variance(0.0, 1.0)]
dist_negative_binomial_cdf	scalar	Computes the cumulative distribution function (CDF) of the negative_binomial distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_negative_binomial_cdf(10, 0.5, 5)]
dist_negative_binomial_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the negative_binomial distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_negative_binomial_cdf_complement(10, 0.5, 5)]
dist_negative_binomial_chf	scalar	Computes the cumulative hazard function of the negative_binomial distribution.	NULL	[dist_negative_binomial_chf(10, 0.5, 5)]
dist_negative_binomial_hazard	scalar	Computes the hazard function of the negative_binomial distribution.	NULL	[dist_negative_binomial_hazard(10, 0.5, 5)]
dist_negative_binomial_kurtosis	scalar	Returns the kurtosis of the negative_binomial distribution.	NULL	[dist_negative_binomial_kurtosis(10, 0.5)]
dist_negative_binomial_kurtosis_excess	scalar	Returns the excess kurtosis of the negative_binomial distribution.	NULL	[dist_negative_binomial_kurtosis_excess(10, 0.5)]
dist_negative_binomial_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the negative_binomial distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_negative_binomial_log_cdf(10, 0.5, 5)]
dist_negative_binomial_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the negative_binomial distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_negative_binomial_log_cdf_complement(10, 0.5, 5)]
dist_negative_binomial_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the negative_binomial distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_negative_binomial_log_pdf(10, 0.5, 5)]
dist_negative_binomial_median	scalar	Returns the median (50th percentile) of the negative_binomial distribution, which equals the mean.	NULL	[dist_negative_binomial_median(10, 0.5)]
dist_negative_binomial_mode	scalar	Returns the mode (most likely value) of the negative_binomial distribution, which equals the mean.	NULL	[dist_negative_binomial_mode(10, 0.5)]
dist_negative_binomial_pdf	scalar	Computes the probability density function (PDF) of the negative_binomial distribution. Returns the probability densityat point x for a negative_binomial distribution with specified parameters.	NULL	[dist_negative_binomial_pdf(10, 0.5, 5)]
dist_negative_binomial_quantile	scalar	Computes the quantile function (inverse CDF) of the negative_binomial distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_negative_binomial_quantile(10, 0.5, 0.95)]
dist_negative_binomial_quantile_complement	scalar	Computes the complementary quantile function of the negative_binomial distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_negative_binomial_quantile_complement(10, 0.5, 0.05)]
dist_negative_binomial_range	scalar	Returns the range of the negative_binomial distribution.	NULL	[dist_negative_binomial_range(10, 0.5)]
dist_negative_binomial_sample	scalar	Generates random samples from the negative_binomial distribution with specified parameters.	NULL	[dist_negative_binomial_sample(10, 0.5)]
dist_negative_binomial_skewness	scalar	Returns the skewness of the negative_binomial distribution.	NULL	[dist_negative_binomial_skewness(10, 0.5)]
dist_negative_binomial_support	scalar	Returns the support of the negative_binomial distribution.	NULL	[dist_negative_binomial_support(10, 0.5)]
dist_negative_binomial_variance	scalar	Returns the variance (σ²) of the negative_binomial distribution.	NULL	[dist_negative_binomial_variance(10, 0.5)]
dist_normal_cdf	scalar	Computes the cumulative distribution function (CDF) of the normal distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_normal_cdf(0, 1.0, 0.5)]
dist_normal_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the normal distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_normal_cdf_complement(0, 1.0, 0.5)]
dist_normal_chf	scalar	Computes the cumulative hazard function of the normal distribution.	NULL	[dist_normal_chf(0, 1.0, 0.5)]
dist_normal_hazard	scalar	Computes the hazard function of the normal distribution.	NULL	[dist_normal_hazard(0, 1.0, 0.5)]
dist_normal_kurtosis	scalar	Returns the kurtosis of the normal distribution.	NULL	[dist_normal_kurtosis(0.0, 1.0)]
dist_normal_kurtosis_excess	scalar	Returns the excess kurtosis of the normal distribution.	NULL	[dist_normal_kurtosis_excess(0.0, 1.0)]
dist_normal_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the normal distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_normal_log_cdf(0, 1.0, 0.5)]
dist_normal_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the normal distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_normal_log_cdf_complement(0, 1.0, 0.5)]
dist_normal_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the normal distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_normal_log_pdf(0, 1.0, 0.5)]
dist_normal_mean	scalar	Returns the mean (μ) of the normal distribution, which is the first moment.	NULL	[dist_normal_mean(0.0, 1.0)]
dist_normal_median	scalar	Returns the median (50th percentile) of the normal distribution, which equals the mean.	NULL	[dist_normal_median(0.0, 1.0)]
dist_normal_mode	scalar	Returns the mode (most likely value) of the normal distribution, which equals the mean.	NULL	[dist_normal_mode(0.0, 1.0)]
dist_normal_pdf	scalar	Computes the probability density function (PDF) of the normal distribution. Returns the probability densityat point x for a normal distribution with specified parameters.	NULL	[dist_normal_pdf(0, 1.0, 0.5)]
dist_normal_quantile	scalar	Computes the quantile function (inverse CDF) of the normal distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_normal_quantile(0, 1.0, 0.95)]
dist_normal_quantile_complement	scalar	Computes the complementary quantile function of the normal distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_normal_quantile_complement(0, 1.0, 0.95)]
dist_normal_range	scalar	Returns the range of the normal distribution.	NULL	[dist_normal_range(0.0, 1.0)]
dist_normal_sample	scalar	Generates random samples from the normal distribution with specified parameters.	NULL	[dist_normal_sample(0.0, 1.0)]
dist_normal_skewness	scalar	Returns the skewness of the normal distribution.	NULL	[dist_normal_skewness(0.0, 1.0)]
dist_normal_stddev	scalar	Returns the standard deviation (σ) of the normal distribution.	NULL	[dist_normal_stddev(0.0, 1.0)]
dist_normal_support	scalar	Returns the support of the normal distribution.	NULL	[dist_normal_support(0.0, 1.0)]
dist_normal_variance	scalar	Returns the variance (σ²) of the normal distribution.	NULL	[dist_normal_variance(0.0, 1.0)]
dist_pareto_cdf	scalar	Computes the cumulative distribution function (CDF) of the pareto distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_pareto_cdf(3.0, 1.0, 1.5)]
dist_pareto_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the pareto distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_pareto_cdf_complement(3.0, 1.0, 1.5)]
dist_pareto_chf	scalar	Computes the cumulative hazard function of the pareto distribution.	NULL	[dist_pareto_chf(3.0, 1.0, 1.5)]
dist_pareto_hazard	scalar	Computes the hazard function of the pareto distribution.	NULL	[dist_pareto_hazard(3.0, 1.0, 1.5)]
dist_pareto_kurtosis	scalar	Returns the kurtosis of the pareto distribution.	NULL	[dist_pareto_kurtosis(3.0, 1.0)]
dist_pareto_kurtosis_excess	scalar	Returns the excess kurtosis of the pareto distribution.	NULL	[dist_pareto_kurtosis_excess(3.0, 1.0)]
dist_pareto_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the pareto distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_pareto_log_cdf(3.0, 1.0, 1.5)]
dist_pareto_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the pareto distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_pareto_log_cdf_complement(3.0, 1.0, 1.5)]
dist_pareto_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the pareto distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_pareto_log_pdf(3.0, 1.0, 1.5)]
dist_pareto_mean	scalar	Returns the mean (μ) of the pareto distribution, which is the first moment.	NULL	[dist_pareto_mean(3.0, 1.0)]
dist_pareto_median	scalar	Returns the median (50th percentile) of the pareto distribution, which equals the mean.	NULL	[dist_pareto_median(3.0, 1.0)]
dist_pareto_mode	scalar	Returns the mode (most likely value) of the pareto distribution, which equals the mean.	NULL	[dist_pareto_mode(3.0, 1.0)]
dist_pareto_pdf	scalar	Computes the probability density function (PDF) of the pareto distribution. Returns the probability densityat point x for a pareto distribution with specified parameters.	NULL	[dist_pareto_pdf(3.0, 1.0, 1.5)]
dist_pareto_quantile	scalar	Computes the quantile function (inverse CDF) of the pareto distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_pareto_quantile(3.0, 1.0, 0.95)]
dist_pareto_quantile_complement	scalar	Computes the complementary quantile function of the pareto distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_pareto_quantile_complement(3.0, 1.0, 0.05)]
dist_pareto_range	scalar	Returns the range of the pareto distribution.	NULL	[dist_pareto_range(3.0, 1.0)]
dist_pareto_skewness	scalar	Returns the skewness of the pareto distribution.	NULL	[dist_pareto_skewness(3.0, 1.0)]
dist_pareto_stddev	scalar	Returns the standard deviation (σ) of the pareto distribution.	NULL	[dist_pareto_stddev(3.0, 1.0)]
dist_pareto_support	scalar	Returns the support of the pareto distribution.	NULL	[dist_pareto_support(3.0, 1.0)]
dist_pareto_variance	scalar	Returns the variance (σ²) of the pareto distribution.	NULL	[dist_pareto_variance(3.0, 1.0)]
dist_poisson_cdf	scalar	Computes the cumulative distribution function (CDF) of the poisson distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_poisson_cdf(5.0, 3)]
dist_poisson_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the poisson distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_poisson_cdf_complement(5.0, 3)]
dist_poisson_chf	scalar	Computes the cumulative hazard function of the poisson distribution.	NULL	[dist_poisson_chf(5.0, 3)]
dist_poisson_hazard	scalar	Computes the hazard function of the poisson distribution.	NULL	[dist_poisson_hazard(5.0, 3)]
dist_poisson_kurtosis	scalar	Returns the kurtosis of the poisson distribution.	NULL	[dist_poisson_kurtosis(5.0)]
dist_poisson_kurtosis_excess	scalar	Returns the excess kurtosis of the poisson distribution.	NULL	[dist_poisson_kurtosis_excess(5.0)]
dist_poisson_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the poisson distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_poisson_log_cdf(5.0, 3)]
dist_poisson_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the poisson distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_poisson_log_cdf_complement(5.0, 3)]
dist_poisson_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the poisson distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_poisson_log_pdf(5.0, 3)]
dist_poisson_mean	scalar	Returns the mean (μ) of the poisson distribution, which is the first moment.	NULL	[dist_poisson_mean(5.0)]
dist_poisson_median	scalar	Returns the median (50th percentile) of the poisson distribution, which equals the mean.	NULL	[dist_poisson_median(5.0)]
dist_poisson_mode	scalar	Returns the mode (most likely value) of the poisson distribution, which equals the mean.	NULL	[dist_poisson_mode(5.0)]
dist_poisson_pdf	scalar	Computes the probability density function (PDF) of the poisson distribution. Returns the probability densityat point x for a poisson distribution with specified parameters.	NULL	[dist_poisson_pdf(5.0, 3)]
dist_poisson_quantile	scalar	Computes the quantile function (inverse CDF) of the poisson distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_poisson_quantile(5.0, 0.95)]
dist_poisson_quantile_complement	scalar	Computes the complementary quantile function of the poisson distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_poisson_quantile_complement(5.0, 0.05)]
dist_poisson_range	scalar	Returns the range of the poisson distribution.	NULL	[dist_poisson_range(5.0)]
dist_poisson_sample	scalar	Generates random samples from the poisson distribution with specified parameters.	NULL	[dist_poisson_sample(5.0)]
dist_poisson_skewness	scalar	Returns the skewness of the poisson distribution.	NULL	[dist_poisson_skewness(5.0)]
dist_poisson_stddev	scalar	Returns the standard deviation (σ) of the poisson distribution.	NULL	[dist_poisson_stddev(5.0)]
dist_poisson_support	scalar	Returns the support of the poisson distribution.	NULL	[dist_poisson_support(5.0)]
dist_poisson_variance	scalar	Returns the variance (σ²) of the poisson distribution.	NULL	[dist_poisson_variance(5.0)]
dist_rayleigh_cdf	scalar	Computes the cumulative distribution function (CDF) of the rayleigh distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_rayleigh_cdf(1.0, 0.5)]
dist_rayleigh_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the rayleigh distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_rayleigh_cdf_complement(1.0, 0.5)]
dist_rayleigh_chf	scalar	Computes the cumulative hazard function of the rayleigh distribution.	NULL	[dist_rayleigh_chf(1.0, 0.5)]
dist_rayleigh_hazard	scalar	Computes the hazard function of the rayleigh distribution.	NULL	[dist_rayleigh_hazard(1.0, 0.5)]
dist_rayleigh_kurtosis	scalar	Returns the kurtosis of the rayleigh distribution.	NULL	[dist_rayleigh_kurtosis(1.0)]
dist_rayleigh_kurtosis_excess	scalar	Returns the excess kurtosis of the rayleigh distribution.	NULL	[dist_rayleigh_kurtosis_excess(1.0)]
dist_rayleigh_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the rayleigh distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_rayleigh_log_cdf(1.0, 0.5)]
dist_rayleigh_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the rayleigh distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_rayleigh_log_cdf_complement(1.0, 0.5)]
dist_rayleigh_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the rayleigh distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_rayleigh_log_pdf(1.0, 0.5)]
dist_rayleigh_mean	scalar	Returns the mean (μ) of the rayleigh distribution, which is the first moment.	NULL	[dist_rayleigh_mean(1.0)]
dist_rayleigh_median	scalar	Returns the median (50th percentile) of the rayleigh distribution, which equals the mean.	NULL	[dist_rayleigh_median(1.0)]
dist_rayleigh_mode	scalar	Returns the mode (most likely value) of the rayleigh distribution, which equals the mean.	NULL	[dist_rayleigh_mode(1.0)]
dist_rayleigh_pdf	scalar	Computes the probability density function (PDF) of the rayleigh distribution. Returns the probability densityat point x for a rayleigh distribution with specified parameters.	NULL	[dist_rayleigh_pdf(1.0, 0.5)]
dist_rayleigh_quantile	scalar	Computes the quantile function (inverse CDF) of the rayleigh distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_rayleigh_quantile(1.0, 0.95)]
dist_rayleigh_quantile_complement	scalar	Computes the complementary quantile function of the rayleigh distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_rayleigh_quantile_complement(1.0, 0.05)]
dist_rayleigh_range	scalar	Returns the range of the rayleigh distribution.	NULL	[dist_rayleigh_range(1.0)]
dist_rayleigh_skewness	scalar	Returns the skewness of the rayleigh distribution.	NULL	[dist_rayleigh_skewness(1.0)]
dist_rayleigh_stddev	scalar	Returns the standard deviation (σ) of the rayleigh distribution.	NULL	[dist_rayleigh_stddev(1.0)]
dist_rayleigh_support	scalar	Returns the support of the rayleigh distribution.	NULL	[dist_rayleigh_support(1.0)]
dist_rayleigh_variance	scalar	Returns the variance (σ²) of the rayleigh distribution.	NULL	[dist_rayleigh_variance(1.0)]
dist_students_t_cdf	scalar	Computes the cumulative distribution function (CDF) of the students_t distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_students_t_cdf(10, 1.5)]
dist_students_t_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the students_t distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_students_t_cdf_complement(10, 1.5)]
dist_students_t_chf	scalar	Computes the cumulative hazard function of the students_t distribution.	NULL	[dist_students_t_chf(10, 1.5)]
dist_students_t_hazard	scalar	Computes the hazard function of the students_t distribution.	NULL	[dist_students_t_hazard(10, 1.5)]
dist_students_t_kurtosis	scalar	Returns the kurtosis of the students_t distribution.	NULL	[dist_students_t_kurtosis(10)]
dist_students_t_kurtosis_excess	scalar	Returns the excess kurtosis of the students_t distribution.	NULL	[dist_students_t_kurtosis_excess(10)]
dist_students_t_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the students_t distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_students_t_log_cdf(10, 1.5)]
dist_students_t_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the students_t distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_students_t_log_cdf_complement(10, 1.5)]
dist_students_t_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the students_t distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_students_t_log_pdf(10, 1.5)]
dist_students_t_mean	scalar	Returns the mean (μ) of the students_t distribution, which is the first moment.	NULL	[dist_students_t_mean(10)]
dist_students_t_median	scalar	Returns the median (50th percentile) of the students_t distribution, which equals the mean.	NULL	[dist_students_t_median(10)]
dist_students_t_mode	scalar	Returns the mode (most likely value) of the students_t distribution, which equals the mean.	NULL	[dist_students_t_mode(10)]
dist_students_t_pdf	scalar	Computes the probability density function (PDF) of the students_t distribution. Returns the probability densityat point x for a students_t distribution with specified parameters.	NULL	[dist_students_t_pdf(10, 1.5)]
dist_students_t_quantile	scalar	Computes the quantile function (inverse CDF) of the students_t distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_students_t_quantile(10, 0.95)]
dist_students_t_quantile_complement	scalar	Computes the complementary quantile function of the students_t distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_students_t_quantile_complement(10, 0.05)]
dist_students_t_range	scalar	Returns the range of the students_t distribution.	NULL	[dist_students_t_range(10)]
dist_students_t_sample	scalar	Generates random samples from the students_t distribution with specified parameters.	NULL	[dist_students_t_sample(10)]
dist_students_t_skewness	scalar	Returns the skewness of the students_t distribution.	NULL	[dist_students_t_skewness(10)]
dist_students_t_stddev	scalar	Returns the standard deviation (σ) of the students_t distribution.	NULL	[dist_students_t_stddev(10)]
dist_students_t_support	scalar	Returns the support of the students_t distribution.	NULL	[dist_students_t_support(10)]
dist_students_t_variance	scalar	Returns the variance (σ²) of the students_t distribution.	NULL	[dist_students_t_variance(10)]
dist_uniform_int_cdf	scalar	Computes the cumulative distribution function (CDF) of the uniform_int distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_uniform_int_cdf(1, 6, 3)]
dist_uniform_int_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the uniform_int distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_uniform_int_cdf_complement(1, 6, 3)]
dist_uniform_int_chf	scalar	Computes the cumulative hazard function of the uniform_int distribution.	NULL	[dist_uniform_int_chf(1, 6, 3)]
dist_uniform_int_hazard	scalar	Computes the hazard function of the uniform_int distribution.	NULL	[dist_uniform_int_hazard(1, 6, 3)]
dist_uniform_int_kurtosis	scalar	Returns the kurtosis of the uniform_int distribution.	NULL	[dist_uniform_int_kurtosis(1, 6)]
dist_uniform_int_kurtosis_excess	scalar	Returns the excess kurtosis of the uniform_int distribution.	NULL	[dist_uniform_int_kurtosis_excess(1, 6)]
dist_uniform_int_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the uniform_int distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_uniform_int_log_cdf(1, 6, 3)]
dist_uniform_int_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the uniform_int distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_uniform_int_log_cdf_complement(1, 6, 3)]
dist_uniform_int_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the uniform_int distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_uniform_int_log_pdf(1, 6, 3)]
dist_uniform_int_mean	scalar	Returns the mean (μ) of the uniform_int distribution, which is the first moment.	NULL	[dist_uniform_int_mean(1, 6)]
dist_uniform_int_median	scalar	Returns the median (50th percentile) of the uniform_int distribution, which equals the mean.	NULL	[dist_uniform_int_median(1, 6)]
dist_uniform_int_mode	scalar	Returns the mode (most likely value) of the uniform_int distribution, which equals the mean.	NULL	[dist_uniform_int_mode(1, 6)]
dist_uniform_int_pdf	scalar	Computes the probability density function (PDF) of the uniform_int distribution. Returns the probability densityat point x for a uniform_int distribution with specified parameters.	NULL	[dist_uniform_int_pdf(1, 6, 3)]
dist_uniform_int_quantile	scalar	Computes the quantile function (inverse CDF) of the uniform_int distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_uniform_int_quantile(1, 6, 0.95)]
dist_uniform_int_quantile_complement	scalar	Computes the complementary quantile function of the uniform_int distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_uniform_int_quantile_complement(1, 6, 0.05)]
dist_uniform_int_range	scalar	Returns the range of the uniform_int distribution.	NULL	[dist_uniform_int_range(1, 6)]
dist_uniform_int_sample	scalar	Generates random samples from the uniform_int distribution with specified parameters.	NULL	[dist_uniform_int_sample(1, 6)]
dist_uniform_int_skewness	scalar	Returns the skewness of the uniform_int distribution.	NULL	[dist_uniform_int_skewness(1, 6)]
dist_uniform_int_stddev	scalar	Returns the standard deviation (σ) of the uniform_int distribution.	NULL	[dist_uniform_int_stddev(1, 6)]
dist_uniform_int_support	scalar	Returns the support of the uniform_int distribution.	NULL	[dist_uniform_int_support(1, 6)]
dist_uniform_int_variance	scalar	Returns the variance (σ²) of the uniform_int distribution.	NULL	[dist_uniform_int_variance(1, 6)]
dist_uniform_real_cdf	scalar	Computes the cumulative distribution function (CDF) of the uniform_real distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_uniform_real_cdf(0, 1.0, 0.5)]
dist_uniform_real_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the uniform_real distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_uniform_real_cdf_complement(0, 1.0, 0.5)]
dist_uniform_real_chf	scalar	Computes the cumulative hazard function of the uniform_real distribution.	NULL	[dist_uniform_real_chf(0, 1.0, 0.5)]
dist_uniform_real_hazard	scalar	Computes the hazard function of the uniform_real distribution.	NULL	[dist_uniform_real_hazard(0, 1.0, 0.5)]
dist_uniform_real_kurtosis	scalar	Returns the kurtosis of the uniform_real distribution.	NULL	[dist_uniform_real_kurtosis(0.0, 1.0)]
dist_uniform_real_kurtosis_excess	scalar	Returns the excess kurtosis of the uniform_real distribution.	NULL	[dist_uniform_real_kurtosis_excess(0.0, 1.0)]
dist_uniform_real_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the uniform_real distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_uniform_real_log_cdf(0, 1.0, 0.5)]
dist_uniform_real_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the uniform_real distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_uniform_real_log_cdf_complement(0, 1.0, 0.5)]
dist_uniform_real_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the uniform_real distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_uniform_real_log_pdf(0, 1.0, 0.5)]
dist_uniform_real_mean	scalar	Returns the mean (μ) of the uniform_real distribution, which is the first moment.	NULL	[dist_uniform_real_mean(0.0, 1.0)]
dist_uniform_real_median	scalar	Returns the median (50th percentile) of the uniform_real distribution, which equals the mean.	NULL	[dist_uniform_real_median(0.0, 1.0)]
dist_uniform_real_mode	scalar	Returns the mode (most likely value) of the uniform_real distribution, which equals the mean.	NULL	[dist_uniform_real_mode(0.0, 1.0)]
dist_uniform_real_pdf	scalar	Computes the probability density function (PDF) of the uniform_real distribution. Returns the probability densityat point x for a uniform_real distribution with specified parameters.	NULL	[dist_uniform_real_pdf(0, 1.0, 0.5)]
dist_uniform_real_quantile	scalar	Computes the quantile function (inverse CDF) of the uniform_real distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_uniform_real_quantile(0, 1.0, 0.95)]
dist_uniform_real_quantile_complement	scalar	Computes the complementary quantile function of the uniform_real distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_uniform_real_quantile_complement(0, 1.0, 0.95)]
dist_uniform_real_range	scalar	Returns the range of the uniform_real distribution.	NULL	[dist_uniform_real_range(0.0, 1.0)]
dist_uniform_real_sample	scalar	Generates random samples from the uniform_real distribution with specified parameters.	NULL	[dist_uniform_real_sample(0.0, 1.0)]
dist_uniform_real_skewness	scalar	Returns the skewness of the uniform_real distribution.	NULL	[dist_uniform_real_skewness(0.0, 1.0)]
dist_uniform_real_stddev	scalar	Returns the standard deviation (σ) of the uniform_real distribution.	NULL	[dist_uniform_real_stddev(0.0, 1.0)]
dist_uniform_real_support	scalar	Returns the support of the uniform_real distribution.	NULL	[dist_uniform_real_support(0.0, 1.0)]
dist_uniform_real_variance	scalar	Returns the variance (σ²) of the uniform_real distribution.	NULL	[dist_uniform_real_variance(0.0, 1.0)]
dist_weibull_cdf	scalar	Computes the cumulative distribution function (CDF) of the weibull distribution. Returns the probability that a random variable X is less than or equal to x.	NULL	[dist_weibull_cdf(1.5, 1.0, 0.5)]
dist_weibull_cdf_complement	scalar	Computes the complementary cumulative distribution function (1 - CDF) of the weibull distribution. Returns the probability that X > x, equivalent to the survival function.	NULL	[dist_weibull_cdf_complement(1.5, 1.0, 0.5)]
dist_weibull_chf	scalar	Computes the cumulative hazard function of the weibull distribution.	NULL	[dist_weibull_chf(1.5, 1.0, 0.5)]
dist_weibull_hazard	scalar	Computes the hazard function of the weibull distribution.	NULL	[dist_weibull_hazard(1.5, 1.0, 0.5)]
dist_weibull_kurtosis	scalar	Returns the kurtosis of the weibull distribution.	NULL	[dist_weibull_kurtosis(1.5, 1.0)]
dist_weibull_kurtosis_excess	scalar	Returns the excess kurtosis of the weibull distribution.	NULL	[dist_weibull_kurtosis_excess(1.5, 1.0)]
dist_weibull_log_cdf	scalar	Computes the natural logarithm of the cumulative distribution function (CDF) of the weibull distribution. Returns the logarithm of the probability that a random variable X is less than or equal to x.	NULL	[dist_weibull_log_cdf(1.5, 1.0, 0.5)]
dist_weibull_log_cdf_complement	scalar	Computes the natural logarithm of the complementary cumulative distribution function (1 - CDF) of the weibull distribution. Returns the logarithm of the probability that X > x, equivalent to the survival function.	NULL	[dist_weibull_log_cdf_complement(1.5, 1.0, 0.5)]
dist_weibull_log_pdf	scalar	Computes the natural logarithm of the probability density function (log-PDF) of the weibull distribution. Useful for numerical stability when dealing with very small probabilities.	NULL	[dist_weibull_log_pdf(1.5, 1.0, 0.5)]
dist_weibull_median	scalar	Returns the median (50th percentile) of the weibull distribution, which equals the mean.	NULL	[dist_weibull_median(1.5, 1.0)]
dist_weibull_mode	scalar	Returns the mode (most likely value) of the weibull distribution, which equals the mean.	NULL	[dist_weibull_mode(1.5, 1.0)]
dist_weibull_pdf	scalar	Computes the probability density function (PDF) of the weibull distribution. Returns the probability densityat point x for a weibull distribution with specified parameters.	NULL	[dist_weibull_pdf(1.5, 1.0, 0.5)]
dist_weibull_quantile	scalar	Computes the quantile function (inverse CDF) of the weibull distribution. Returns the value x such that P(X ≤ x) = p, where p is the cumulative probability.	NULL	[dist_weibull_quantile(1.5, 1.0, 0.95)]
dist_weibull_quantile_complement	scalar	Computes the complementary quantile function of the weibull distribution. Returns the value x such that P(X > x) = p, useful for computing upper tail quantiles.	NULL	[dist_weibull_quantile_complement(1.5, 1.0, 0.05)]
dist_weibull_range	scalar	Returns the range of the weibull distribution.	NULL	[dist_weibull_range(1.5, 1.0)]
dist_weibull_sample	scalar	Generates random samples from the weibull distribution with specified parameters.	NULL	[dist_weibull_sample(1.5, 1.0)]
dist_weibull_skewness	scalar	Returns the skewness of the weibull distribution.	NULL	[dist_weibull_skewness(1.5, 1.0)]
dist_weibull_support	scalar	Returns the support of the weibull distribution.	NULL	[dist_weibull_support(1.5, 1.0)]
dist_weibull_variance	scalar	Returns the variance (σ²) of the weibull distribution.	NULL	[dist_weibull_variance(1.5, 1.0)]

Added Settings

name	description	input_type	scope	aliases
auto_fallback_to_full_download	Allows automatically falling back to full file downloads when possible.	BOOLEAN	GLOBAL	[]
ca_cert_file	Path to a custom certificate file for self-signed certificates.	VARCHAR	GLOBAL	[]
enable_curl_server_cert_verification	Enable server side certificate verification for CURL backend.	BOOLEAN	GLOBAL	[]
enable_server_cert_verification	Enable server side certificate verification.	BOOLEAN	GLOBAL	[]
force_download	Forces upfront download of file	BOOLEAN	GLOBAL	[]
hf_max_per_page	Debug option to limit number of items returned in list requests	UBIGINT	GLOBAL	[]
http_keep_alive	Keep alive connections. Setting this to false can help when running into connection failures	BOOLEAN	GLOBAL	[]
http_retries	HTTP retries on I/O error	UBIGINT	GLOBAL	[]
http_retry_backoff	Backoff factor for exponentially increasing retry wait time	FLOAT	GLOBAL	[]
http_retry_wait_ms	Time between retries	UBIGINT	GLOBAL	[]
http_timeout	HTTP timeout read/write/connection/retry (in seconds)	UBIGINT	GLOBAL	[]
httpfs_client_implementation	Select which is the HTTPUtil implementation to be used	VARCHAR	GLOBAL	[]
merge_http_secret_into_s3_request	Merges http secret params into S3 requests	BOOLEAN	GLOBAL	[]
s3_access_key_id	S3 Access Key ID	VARCHAR	GLOBAL	[]
s3_endpoint	S3 Endpoint	VARCHAR	GLOBAL	[]
s3_kms_key_id	S3 KMS Key ID	VARCHAR	GLOBAL	[]
s3_region	S3 Region	VARCHAR	GLOBAL	[]
s3_requester_pays	S3 use requester pays mode	BOOLEAN	GLOBAL	[]
s3_secret_access_key	S3 Access Key	VARCHAR	GLOBAL	[]
s3_session_token	S3 Session Token	VARCHAR	GLOBAL	[]
s3_uploader_max_filesize	S3 Uploader max filesize (between 50GB and 5TB)	VARCHAR	GLOBAL	[]
s3_uploader_max_parts_per_file	S3 Uploader max parts per file (between 1 and 10000)	UBIGINT	GLOBAL	[]
s3_uploader_thread_limit	S3 Uploader global thread limit	UBIGINT	GLOBAL	[]
s3_url_compatibility_mode	Disable Globs and Query Parameters on S3 URLs	BOOLEAN	GLOBAL	[]
s3_url_style	S3 URL style	VARCHAR	GLOBAL	[]
s3_use_ssl	S3 use SSL	BOOLEAN	GLOBAL	[]
unsafe_disable_etag_checks	Disable checks on ETag consistency	BOOLEAN	GLOBAL	[]

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