SQL functions for evaluating probability functions. More...

Functions
float8	bernoulli_cdf (float8 x, float8 sp)
	Bernoulli cumulative distribution function. More...

float8	bernoulli_pmf (int4 x, float8 sp)
	Bernoulli probability mass function. More...

float8	bernoulli_quantile (float8 p, float8 sp)
	Bernoulli quantile function. More...

float8	beta_cdf (float8 x, float8 alpha, float8 beta)
	Beta cumulative distribution function. More...

float8	beta_pdf (float8 x, float8 alpha, float8 beta)
	Beta probability density function. More...

float8	beta_quantile (float8 p, float8 alpha, float8 beta)
	Beta quantile function. More...

float8	binomial_cdf (float8 x, int4 n, float8 sp)
	Binomial cumulative distribution function. More...

float8	binomial_pmf (int4 x, int4 n, float8 sp)
	Binomial probability mass function. More...

float8	binomial_quantile (float8 p, int4 n, float8 sp)
	Binomial quantile function. More...

float8	cauchy_cdf (float8 x, float8 location, float8 scale)
	Cauchy cumulative distribution function. More...

float8	cauchy_pdf (float8 x, float8 location, float8 scale)
	Cauchy probability density function. More...

float8	cauchy_quantile (float8 p, float8 location, float8 scale)
	Cauchy quantile function. More...

float8	chi_squared_cdf (float8 x, float8 df)
	Chi-squared cumulative distribution function. More...

float8	chi_squared_pdf (float8 x, float8 df)
	Chi-squared distribution probability density function. More...

float8	chi_squared_quantile (float8 p, float8 df)
	Chi-squared distribution quantile function. More...

float8	exponential_cdf (float8 x, float8 lambda)
	Exponential cumulative distribution function. More...

float8	exponential_pdf (float8 x, float8 lambda)
	Exponential probability density function. More...

float8	exponential_quantile (float8 p, float8 lambda)
	Exponential quantile function. More...

float8	extreme_value_cdf (float8 x, float8 location, float8 scale)
	Extreme Value cumulative distribution function. More...

float8	extreme_value_pdf (float8 x, float8 location, float8 scale)
	Extreme Value probability density function. More...

float8	extreme_value_quantile (float8 p, float8 location, float8 scale)
	Extreme Value quantile function. More...

float8	fisher_f_cdf (float8 x, float8 df1, float8 df2)
	Fisher F cumulative distribution function. More...

float8	fisher_f_pdf (float8 x, float8 df1, float8 df2)
	Fisher F probability density function. More...

float8	fisher_f_quantile (float8 p, float8 df1, float8 df2)
	Fisher F quantile function. More...

float8	gamma_cdf (float8 x, float8 shape, float8 scale)
	Gamma cumulative distribution function. More...

float8	gamma_pdf (float8 x, float8 shape, float8 scale)
	Gamma probability density function. More...

float8	gamma_quantile (float8 p, float8 shape, float8 scale)
	Gamma quantile function. More...

float8	geometric_cdf (float8 x, float8 sp)
	Geometric cumulative distribution function. More...

float8	geometric_pmf (int4 x, float8 sp)
	Geometric probability mass function. More...

float8	geometric_quantile (float8 p, float8 sp)
	Geometric quantile function. More...

float8	hypergeometric_cdf (float8 x, int4 r, int4 n, int4 N)
	Hypergeometric cumulative distribution function. More...

float8	hypergeometric_pmf (int4 x, int4 r, int4 n, int4 N)
	Hypergeometric probability mass function. More...

float8	hypergeometric_quantile (float8 p, int4 r, int4 n, int4 N)
	Hypergeometric quantile function. More...

float8	inverse_gamma_cdf (float8 x, float8 shape, float8 scale)
	Inverse Gamma cumulative distribution function. More...

float8	inverse_gamma_pdf (float8 x, float8 shape, float8 scale)
	Inverse Gamma probability density function. More...

float8	inverse_gamma_quantile (float8 p, float8 shape, float8 scale)
	Inverse Gamma quantile function. More...

float8	kolmogorov_cdf (float8 x)
	Kolmogorov cumulative distribution function. More...

float8	laplace_cdf (float8 x, float8 mean, float8 scale)
	Laplace cumulative distribution function. More...

float8	laplace_pdf (float8 x, float8 mean, float8 scale)
	Laplace probability density function. More...

float8	laplace_quantile (float8 p, float8 mean, float8 scale)
	Laplace quantile function. More...

float8	logistic_cdf (float8 x, float8 mean, float8 scale)
	Logistic cumulative distribution function. More...

float8	logistic_pdf (float8 x, float8 mean, float8 scale)
	Logistic probability density function. More...

float8	logistic_quantile (float8 p, float8 mean, float8 scale)
	Logistic quantile function. More...

float8	lognormal_cdf (float8 x, float8 location, float8 scale)
	Log-normal cumulative distribution function. More...

float8	lognormal_pdf (float8 x, float8 location, float8 scale)
	Log-normal probability density function. More...

float8	lognormal_quantile (float8 p, float8 location, float8 scale)
	Log-normal quantile function. More...

float8	negative_binomial_cdf (float8 x, float8 r, float8 sp)
	Negative binomial cumulative distribution function. More...

float8	negative_binomial_pmf (int4 x, float8 r, float8 sp)
	Negative binomial probability mass function. More...

float8	negative_binomial_quantile (float8 p, float8 r, float8 sp)
	Negative binomial quantile function. More...

float8	non_central_beta_cdf (float8 x, float8 alpha, float8 beta, float8 ncp)
	Noncentral beta cumulative distribution function. More...

float8	non_central_beta_pdf (float8 x, float8 alpha, float8 beta, float8 ncp)
	Noncentral beta probability density function. More...

float8	non_central_beta_quantile (float8 p, float8 alpha, float8 beta, float8 ncp)
	Noncentral beta quantile function. More...

float8	non_central_chi_squared_cdf (float8 x, float8 df, float8 ncp)
	Noncentral chi-squared cumulative distribution function. More...

float8	non_central_chi_squared_pdf (float8 x, float8 df, float8 ncp)
	Noncentral chi-squared distribution probability density function. More...

float8	non_central_chi_squared_quantile (float8 p, float8 df, float8 ncp)
	Noncentral chi-squared distribution quantile function. More...

float8	non_central_f_cdf (float8 x, float8 df1, float8 df2, float8 ncp)
	Noncentral Fisher F cumulative distribution function. More...

float8	non_central_f_pdf (float8 x, float8 df1, float8 df2, float8 ncp)
	Noncentral Fisher F probability density function. More...

float8	non_central_f_quantile (float8 p, float8 df1, float8 df2, float8 ncp)
	Noncentral Fisher F quantile function. More...

float8	non_central_t_cdf (float8 x, float8 df, float8 ncp)
	Noncentral Student-t cumulative distribution function. More...

float8	non_central_t_pdf (float8 x, float8 df, float8 ncp)
	Noncentral Student-t probability density function. More...

float8	non_central_t_quantile (float8 p, float8 df, float8 ncp)
	Noncentral Student-t quantile function. More...

float8	normal_cdf (float8 x, float8 mean=0, float8 sd=1)
	Normal cumulative distribution function. More...

float8	normal_cdf (float8 x, float8 mean)

float8	normal_cdf (float8 x)

float8	normal_pdf (float8 x, float8 mean=0, float8 sd=1)
	Normal probability density function. More...

float8	normal_pdf (float8 x, float8 mean)

float8	normal_pdf (float8 x)

float8	normal_quantile (float8 p, float8 mean=0, float8 sd=1)
	Normal quantile function. More...

float8	normal_quantile (float8 p, float8 mean)

float8	normal_quantile (float8 p)

float8	pareto_cdf (float8 x, float8 scale, float8 shape)
	Pareto cumulative distribution function. More...

float8	pareto_pdf (float8 x, float8 scale, float8 shape)
	Pareto probability density function. More...

float8	pareto_quantile (float8 p, float8 scale, float8 shape)
	Pareto quantile function. More...

float8	poisson_cdf (float8 x, float8 mean)
	Poisson cumulative distribution function. More...

float8	poisson_pmf (int4 x, float8 mean)
	Poisson probability mass function. More...

float8	poisson_quantile (float8 p, float8 mean)
	Poisson quantile function. More...

float8	rayleigh_cdf (float8 x, float8 scale)
	Rayleigh cumulative distribution function. More...

float8	rayleigh_pdf (float8 x, float8 scale)
	Rayleigh probability density function. More...

float8	rayleigh_quantile (float8 p, float8 scale)
	Rayleigh quantile function. More...

float8	students_t_cdf (float8 x, float8 df)
	Student's t cumulative distribution function. More...

float8	students_t_pdf (float8 x, float8 df)
	Student's t probability density function. More...

float8	students_t_quantile (float8 p, float8 df)
	Student's t quantile function. More...

float8	triangular_cdf (float8 x, float8 lower, float8 mode, float8 upper)
	Triangular cumulative distribution function. More...

float8	triangular_pdf (float8 x, float8 lower, float8 mode, float8 upper)
	Triangular probability density function. More...

float8	triangular_quantile (float8 p, float8 lower, float8 mode, float8 upper)
	Triangular quantile function. More...

float8	uniform_cdf (float8 x, float8 lower, float8 upper)
	Uniform cumulative distribution function. More...

float8	uniform_pdf (float8 x, float8 lower, float8 upper)
	Uniform probability density function. More...

float8	uniform_quantile (float8 p, float8 lower, float8 upper)
	Uniform quantile function. More...

float8	weibull_cdf (float8 x, float8 shape, float8 scale)
	Weibull cumulative distribution function. More...

float8	weibull_pdf (float8 x, float8 shape, float8 scale)
	Weibull probability density function. More...

float8	weibull_quantile (float8 p, float8 shape, float8 scale)
	Weibull quantile function. More...

Detailed Description

See also: For an overview of probability functions, see the module description Probability Functions.

Function Documentation

◆ bernoulli_cdf()

float8 bernoulli_cdf	(	float8	x,
		float8	sp
	)

Parameters

x	Random variate
sp	Success probability $p \in [0,1]$

Returns: $\Pr[X \leq x]$ where is a Bernoulli-distributed random variable with success probability $\mathit{sp}$

◆ bernoulli_pmf()

float8 bernoulli_pmf	(	int4	x,
		float8	sp
	)

Parameters

x	Random variate
sp	Success probability $\mathit{sp} \in [0,1]$

Returns: where is the probability mass function of a Bernoulli-distributed random variable with success probability $\mathit{sp}$

◆ bernoulli_quantile()

float8 bernoulli_quantile	(	float8	p,
		float8	sp
	)

Parameters

p	Probability $p \in [0,1]$
sp	Success probability $\mathit{sp} \in [0,1]$

Returns: 0 if $p \leq 1 - \mathit{sp}$ and 1 otherwise

◆ beta_cdf()

float8 beta_cdf	(	float8	x,
		float8	alpha,
		float8	beta
	)

Parameters

x	Random variate
alpha	Shape $\alpha > 0$
beta	Shape $\beta > 0$

Returns: $\Pr[X \leq x]$ where is a beta distributed random variable with shape parameters $\alpha$ and $\beta$

◆ beta_pdf()

float8 beta_pdf	(	float8	x,
		float8	alpha,
		float8	beta
	)

Parameters

x	Random variate
alpha	Shape $\alpha > 0$
beta	Shape $\beta > 0$

Returns: where is the probability density function of a beta random variable with shape parameters $\alpha$ and $\beta$

◆ beta_quantile()

float8 beta_quantile	(	float8	p,
		float8	alpha,
		float8	beta
	)

Parameters

p	Probability $p \in [0,1]$
alpha	Shape $\alpha > 0$
beta	Shape $\beta > 0$

Returns: such that $p = \Pr[X \leq x]$ where is beta distribution random variable with shape parameters $\alpha$ and $\beta$

◆ binomial_cdf()

float8 binomial_cdf	(	float8	x,
		int4	n,
		float8	sp
	)

Parameters

x	Random variate
n	The number of trials $n \in \mathbb N_0$
sp	Success probability $\mathit{sp} \in [0,1]$

Returns: $\Pr[X \leq x]$ where is a binomially distributed random variable with trials and success probability $\mathit{sp}$

◆ binomial_pmf()

float8 binomial_pmf	(	int4	x,
		int4	n,
		float8	sp
	)

Parameters

x	Random variate
n	The number of trials $n \in \mathbb N_0$
sp	Success probability $\mathit{sp} \in [0,1]$

Returns: where is the probability mass function of a binomially distributed random variable with trials and success probability $\mathit{sp}$

◆ binomial_quantile()

float8 binomial_quantile	(	float8	p,
		int4	n,
		float8	sp
	)

Parameters

p	Probability $p \in [0,1]$
n	The number of trials $n \in \mathbb N_0$
sp	Success probability $\mathit{sp} \in [0,1]$

Returns: If the maximum such that $p \geq \Pr[X \leq x]$ . If $p \geq 0.5$ the minimum such that $p \leq \Pr[X \leq x]$ . Here, is a binomially distributed random variable with trials and success probability $\mathit{sp}$ .

◆ cauchy_cdf()

float8 cauchy_cdf	(	float8	x,
		float8	location,
		float8	scale
	)

Parameters

x	Random variate
location	Location
scale	Scale $\gamma > 0$

Returns: $\Pr[X \leq x]$ where is a Cauchy-distributed random variable with location and scale parameters and $\gamma$ , respectively

◆ cauchy_pdf()

float8 cauchy_pdf	(	float8	x,
		float8	location,
		float8	scale
	)

Parameters

x	Random variate
location	Location
scale	Scale $\gamma > 0$

Returns: where is the probability density function of a Cauchy-distributed random variable with location and scale parameters and $\gamma$ , respectively

◆ cauchy_quantile()

float8 cauchy_quantile	(	float8	p,
		float8	location,
		float8	scale
	)

Parameters

p	Probability $p \in [0,1]$
location	Location
scale	Scale $\gamma > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a Cauchy-distributed random variable with location and scale parameters and $\gamma$ , respectively

◆ chi_squared_cdf()

float8 chi_squared_cdf	(	float8	x,
		float8	df
	)

Parameters

x	Random variate
df	Degrees of freedom $\nu > 0$

Returns: $\Pr[X \leq x]$ where is a chi-squared distributed random variable with $\nu$ degrees of freedom

◆ chi_squared_pdf()

float8 chi_squared_pdf	(	float8	x,
		float8	df
	)

Parameters

x	Random variate
df	Degrees of freedom $\nu > 0$

Returns: where is the probability density function of a chi-squared distributed random variable with $\nu$ degrees of freedom

◆ chi_squared_quantile()

float8 chi_squared_quantile	(	float8	p,
		float8	df
	)

Parameters

p	Probability $p \in [0,1]$
df	Degrees of freedom $\mu > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a chi-squared distributed random variable with $\nu$ degrees of freedom

◆ exponential_cdf()

float8 exponential_cdf	(	float8	x,
		float8	lambda
	)

Parameters

x	Random variate
lambda	Rate parameter $\lambda > 0$

Returns: $\Pr[X \leq x]$ where is an exponentially distributed random variable with rate parameter $\lambda$

◆ exponential_pdf()

float8 exponential_pdf	(	float8	x,
		float8	lambda
	)

Parameters

x	Random variate
lambda	Rate parameter $\lambda > 0$

Returns: where is the probability density function of exponentially distributed random variable with rate parameter $\lambda$

◆ exponential_quantile()

float8 exponential_quantile	(	float8	p,
		float8	lambda
	)

Parameters

p	Probability $p \in [0,1]$
lambda	Rate parameter $\lambda > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a exponentially distributed random variable with rate parameter $\lambda$

◆ extreme_value_cdf()

float8 extreme_value_cdf	(	float8	x,
		float8	location,
		float8	scale
	)

Parameters

x	Random variate
location	Location $\alpha$
scale	Scale $\beta > 0$

Returns: $\Pr[X \leq x]$ where is an extreme-value distributed random variable with location and scale parameters $\alpha$ and $\beta$ , respectively

◆ extreme_value_pdf()

float8 extreme_value_pdf	(	float8	x,
		float8	location,
		float8	scale
	)

Parameters

x	Random variate
location	Location $\alpha$
scale	Scale $\beta > 0$

Returns: where is the probability density function of an extreme-value distributed random variable with location and scale parameters $\alpha$ and $\beta$ , respectively

◆ extreme_value_quantile()

float8 extreme_value_quantile	(	float8	p,
		float8	location,
		float8	scale
	)

Parameters

p	Probability $p \in [0,1]$
location	Location $\alpha$
scale	Scale $\beta > 0$

Returns: such that $p = \Pr[X \leq x]$ where is an extreme-value distributed random variable with location and scale parameters $\alpha$ and $\beta$ , respectively

◆ fisher_f_cdf()

float8 fisher_f_cdf	(	float8	x,
		float8	df1,
		float8	df2
	)

Parameters

x	Random variate
df1	Degrees of freedom in numerator $\nu_1 > 0$
df2	Degrees of freedom in denominator $\nu_1 > 0$

Returns: $\Pr[X \leq x]$ where is a Fisher F-distributed random variable with parameters $\nu_1$ and $\nu_2$

◆ fisher_f_pdf()

float8 fisher_f_pdf	(	float8	x,
		float8	df1,
		float8	df2
	)

Parameters

x	Random variate
df1	Degrees of freedom in numerator $\nu_1 > 0$
df2	Degrees of freedom in denominator $\nu_1 > 0$

Returns: where is the probability density function of a Fisher F-distributed random variable with parameters $\nu_1$ and $\nu_2$

◆ fisher_f_quantile()

float8 fisher_f_quantile	(	float8	p,
		float8	df1,
		float8	df2
	)

Parameters

p	Probability $p \in [0,1]$
df1	Degrees of freedom in numerator $\nu_1 > 0$
df2	Degrees of freedom in denominator $\nu_1 > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a Fisher F-distributed random variable with parameters $\nu_1$ and $\nu_2$

◆ gamma_cdf()

float8 gamma_cdf	(	float8	x,
		float8	shape,
		float8	scale
	)

Parameters

x	Random variate
shape	Shape
scale	Scale $\theta > 0$

Returns: $\Pr[X \leq x]$ where is a gamma distributed random variable with shape and scale parameters and $\theta$ , respectively

◆ gamma_pdf()

float8 gamma_pdf	(	float8	x,
		float8	shape,
		float8	scale
	)

Parameters

x	Random variate
shape	Shape
scale	Scale $\theta > 0$

Returns: where is the probability density function of a gamma distributed random variable with shape and scale parameters and $\theta$ , respectively

◆ gamma_quantile()

float8 gamma_quantile	(	float8	p,
		float8	shape,
		float8	scale
	)

Parameters

p	Probability $p \in [0,1]$
shape	Shape
scale	Scale $\theta > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a gamma distributed random variable with shape and scale parameters and $\theta$ , respectively

◆ geometric_cdf()

float8 geometric_cdf	(	float8	x,
		float8	sp
	)

Parameters

x	Random variate
sp	Success probability $\mathit{sp} \in [0,1]$

Returns: $\Pr[X \leq x]$ where is a geometrically distributed random variable with success probability $\mathit{sp}$ .

◆ geometric_pmf()

float8 geometric_pmf	(	int4	x,
		float8	sp
	)

Parameters

x	Random variate
sp	Success probability $\mathit{sp} \in [0,1]$

Returns: where is the probability mass function of a geometrically distributed random variable with success probability $\mathit{sp}$

◆ geometric_quantile()

float8 geometric_quantile	(	float8	p,
		float8	sp
	)

Parameters

p	Probability $p \in [0,1]$
sp	Success probability $\mathit{sp} \in [0,1]$

Returns: If the maximum such that $p \geq \Pr[X \leq x]$ . If $p \geq 0.5$ the minimum such that $p \leq \Pr[X \leq x]$ . Here, is a geometrically distributed random variable with success probability $\mathit{sp}$ .

◆ hypergeometric_cdf()

float8 hypergeometric_cdf	(	float8	x,
		int4	r,
		int4	n,
		int4	N
	)

Parameters

x	Random variate
r	Number $r \in \{ 0, 1, \dots, N \}$ of items with distinct property (sometimes called the number of success states in population)
n	Number $n \in \{ 0, 1, \dots, N \}$ of draws (without replacement)
N	Total number $N \in \mathbb N$ of items

Returns: $\Pr[X \leq x]$ where is a hypergeometrically distributed random variable with parameters

◆ hypergeometric_pmf()

float8 hypergeometric_pmf	(	int4	x,
		int4	r,
		int4	n,
		int4	N
	)

Parameters

x	Random variate
r	Number $r \in \{ 0, 1, \dots, N \}$ of items with distinct property (sometimes called the number of success states in population)
n	Number $n \in \{ 0, 1, \dots, N \}$ of draws (without replacement)
N	Total number $N \in \mathbb N$ of items

Returns: where is the probability mass function of a hypergeometrically distributed random variable with parameters

◆ hypergeometric_quantile()

float8 hypergeometric_quantile	(	float8	p,
		int4	r,
		int4	n,
		int4	N
	)

Parameters

p	Probability $p \in [0,1]$
r	Number $r \in \{ 0, 1, \dots, N \}$ of items with distinct property (sometimes called the number of success states in population)
n	Number $n \in \{ 0, 1, \dots, N \}$ of draws (without replacement)
N	Total number $N \in \mathbb N$ of items

Returns: such that $p = \Pr[X \leq x]$ where is a hypergeometrically distributed random variable with parameters

◆ inverse_gamma_cdf()

float8 inverse_gamma_cdf	(	float8	x,
		float8	shape,
		float8	scale
	)

Parameters

x	Random variate
shape	Shape $\alpha > 0$
scale	Scale $\beta > 0$

Returns: $\Pr[X \leq x]$ where is an inverse-gamma distributed random variable with shape and scale parameters $\alpha$ and $\beta$ , respectively

◆ inverse_gamma_pdf()

float8 inverse_gamma_pdf	(	float8	x,
		float8	shape,
		float8	scale
	)

Parameters

x	Random variate
shape	Shape $\alpha > 0$
scale	Scale $\beta > 0$

Returns: where is the probability density function of an inverse-gamma distributed random variable with shape and scale parameters $\alpha$ and $\beta$ , respectively

◆ inverse_gamma_quantile()

float8 inverse_gamma_quantile	(	float8	p,
		float8	shape,
		float8	scale
	)

Parameters

p	Probability $p \in [0,1]$
shape	Shape $\alpha > 0$
scale	Scale $\beta > 0$

Returns: such that $p = \Pr[X \leq x]$ where is an inverse-gamma distributed random variable with shape and scale parameters $\alpha$ and $\beta$ , respectively

◆ kolmogorov_cdf()

float8 kolmogorov_cdf ( float8 x )

Parameters

x	Random variate

Returns: $\Pr[X \leq x]$ where is a Kolmogorov distributed random variable

See also: Kolmogorov-Smirnov test: ks_test()

◆ laplace_cdf()

float8 laplace_cdf	(	float8	x,
		float8	mean,
		float8	scale
	)

Parameters

x	Random variate
mean	Mean $\mu$
scale	Scale

Returns: $\Pr[X \leq x]$ where is a Laplace-distributed random variable with mean $\mu$ and variance

◆ laplace_pdf()

float8 laplace_pdf	(	float8	x,
		float8	mean,
		float8	scale
	)

Parameters

x	Random variate
mean	Mean $\mu$
scale	Scale

Returns: where is the probability density function of a Laplace-distributed random variable with mean $\mu$ and variance

◆ laplace_quantile()

float8 laplace_quantile	(	float8	p,
		float8	mean,
		float8	scale
	)

Parameters

p	Probability $p \in [0,1]$
mean	Mean $\mu$
scale	Scale

Returns: such that $p = \Pr[X \leq x]$ where is a Laplace-distributed random variable with mean $\mu$ and variance

◆ logistic_cdf()

float8 logistic_cdf	(	float8	x,
		float8	mean,
		float8	scale
	)

Parameters

x	Random variate
mean	Mean $\mu$
scale	Scale

Returns: $\Pr[X \leq x]$ where is a logistically distributed random variable with mean $\mu$ and scale parameter

◆ logistic_pdf()

float8 logistic_pdf	(	float8	x,
		float8	mean,
		float8	scale
	)

Parameters

x	Random variate
mean	Mean $\mu$
scale	Scale

Returns: where is the probability density function of a logistically distributed random variable with mean $\mu$ and scale parameter

◆ logistic_quantile()

float8 logistic_quantile	(	float8	p,
		float8	mean,
		float8	scale
	)

Parameters

p	Probability $p \in [0,1]$
mean	Mean $\mu$
scale	Scale

Returns: such that $p = \Pr[X \leq x]$ where is a logistically distributed random variable with mean $\mu$ and scale parameter

◆ lognormal_cdf()

float8 lognormal_cdf	(	float8	x,
		float8	location,
		float8	scale
	)

Parameters

x	Random variate
location	Location
scale	Scale

Returns: $\Pr[X \leq x]$ where is a lognormally distributed random variable with location and scale parameters and , respectively

◆ lognormal_pdf()

float8 lognormal_pdf	(	float8	x,
		float8	location,
		float8	scale
	)

Parameters

x	Random variate
location	Location
scale	Scale

Returns: where is the probability density function of a lognormally distributed random variable with location and scale parameters and , respectively

◆ lognormal_quantile()

float8 lognormal_quantile	(	float8	p,
		float8	location,
		float8	scale
	)

Parameters

p	Probability $p \in [0,1]$
location	Location
scale	Scale

Returns: such that $p = \Pr[X \leq x]$ where is a lognormally distributed random variable with location and scale parameters and , respectively

◆ negative_binomial_cdf()

float8 negative_binomial_cdf	(	float8	x,
		float8	r,
		float8	sp
	)

Parameters

x	Random variate
r	Total number of successes in trials (assuming success in the last trial)
sp	Success probability $\mathit{sp} \in (0,1]$ in each trial

Returns: $\Pr[X \leq x]$ where is a negative-binomially distributed random variable with parameters $r, \mathit{sp}$

◆ negative_binomial_pmf()

float8 negative_binomial_pmf	(	int4	x,
		float8	r,
		float8	sp
	)

Parameters

x	Random variate
r	Total number of successes in trials (assuming success in the last trial)
sp	Success probability $\mathit{sp} \in (0,1]$ in each trial

Returns: where is the probability mass function of a negative-binomially distributed random variable with parameters $r, \mathit{sp}$

◆ negative_binomial_quantile()

float8 negative_binomial_quantile	(	float8	p,
		float8	r,
		float8	sp
	)

Parameters

p	Probability $p \in [0,1]$
r	Total number of successes in trials (assuming success in the last trial)
sp	Success probability $\mathit{sp} \in (0,1]$ in each trial

Returns: If the maximum such that $p \geq \Pr[X \leq x]$ . If $p \geq 0.5$ the minimum such that $p \leq \Pr[X \leq x]$ . Here, is a negative-binomially distributed random variable with parameters $r, \mathit{sp}$

◆ non_central_beta_cdf()

float8 non_central_beta_cdf	(	float8	x,
		float8	alpha,
		float8	beta,
		float8	ncp
	)

Parameters

x	Random variate
alpha	Shape $\alpha > 0$
beta	Shape $\beta > 0$
ncp	Noncentrality parameter $\delta \geq 0$

Returns: $\Pr[X \leq x]$ where is a noncentral-beta distributed random variable with shape parameters and and noncentrality parameter $\delta$

◆ non_central_beta_pdf()

float8 non_central_beta_pdf	(	float8	x,
		float8	alpha,
		float8	beta,
		float8	ncp
	)

Parameters

x	Random variate
alpha	Shape $\alpha > 0$
beta	Shape $\beta > 0$
ncp	Noncentrality parameter $\delta \geq 0$

Returns: where is the probability density function of a noncentral-beta distributed random variable with shape parameters and and noncentrality parameter $\delta$

◆ non_central_beta_quantile()

float8 non_central_beta_quantile	(	float8	p,
		float8	alpha,
		float8	beta,
		float8	ncp
	)

Parameters

p	Probability $p \in [0,1]$
alpha	Shape $\alpha > 0$
beta	Shape $\beta > 0$
ncp	Noncentrality parameter $\delta \geq 0$

Returns: such that $p = \Pr[X \leq x]$ where is a noncentral-beta distributed random variable with shape parameters and and noncentrality parameter $\delta$

◆ non_central_chi_squared_cdf()

float8 non_central_chi_squared_cdf	(	float8	x,
		float8	df,
		float8	ncp
	)

Parameters

x	Random variate
df	Degrees of freedom $\nu > 0$
ncp	The noncentrality parameter $\lambda \geq 0$

Returns: $\Pr[X \leq x]$ where is a noncentral-chi-squared distributed random variable with $\nu$ degrees of freedom and noncentrality parameter $\lambda$

◆ non_central_chi_squared_pdf()

float8 non_central_chi_squared_pdf	(	float8	x,
		float8	df,
		float8	ncp
	)

Parameters

x	Random variate
df	Degrees of freedom $\nu > 0$
ncp	The noncentrality parameter $\lambda \geq 0$

Returns: where is the probability density function of a noncentral-chi-squared distributed random variable with $\nu$ degrees of freedom and noncentrality parameter $\lambda$

◆ non_central_chi_squared_quantile()

float8 non_central_chi_squared_quantile	(	float8	p,
		float8	df,
		float8	ncp
	)

Parameters

p	Probability $p \in [0,1]$
df	Degrees of freedom $\nu > 0$
ncp	The noncentrality parameter $\lambda \geq 0$

Returns: such that $p = \Pr[X \leq x]$ where is a noncentral-chi-squared distributed random variable with $\nu$ degrees of freedom and noncentrality parameter $\lambda$

◆ non_central_f_cdf()

float8 non_central_f_cdf	(	float8	x,
		float8	df1,
		float8	df2,
		float8	ncp
	)

Parameters

x	Random variate
df1	Degrees of freedom in numerator $\nu_1 > 0$
df2	Degrees of freedom in denominator $\nu_1 > 0$
ncp	The noncentrality parameter $\lambda \geq 0$

Returns: $\Pr[X \leq x]$ where is a noncentral Fisher F-distributed random variable with parameters $\nu_1, \nu_2, \lambda$

◆ non_central_f_pdf()

float8 non_central_f_pdf	(	float8	x,
		float8	df1,
		float8	df2,
		float8	ncp
	)

Parameters

x	Random variate
df1	Degrees of freedom in numerator $\nu_1 > 0$
df2	Degrees of freedom in denominator $\nu_1 > 0$
ncp	The noncentrality parameter $\lambda \geq 0$

Returns: where is the probability density function of a noncentral Fisher F-distributed random variable with parameters $\nu_1, \nu_2, \lambda$

◆ non_central_f_quantile()

float8 non_central_f_quantile	(	float8	p,
		float8	df1,
		float8	df2,
		float8	ncp
	)

Parameters

p	Probability $p \in [0,1]$
df1	Degrees of freedom in numerator $\nu_1 > 0$
df2	Degrees of freedom in denominator $\nu_1 > 0$
ncp	The noncentrality parameter $\lambda \geq 0$

Returns: such that $p = \Pr[X \leq x]$ where is a noncentral Fisher F-distributed random variable with parameters $\nu_1, \nu_2, \lambda$

◆ non_central_t_cdf()

float8 non_central_t_cdf	(	float8	x,
		float8	df,
		float8	ncp
	)

Parameters

x	Random variate
df	Degrees of freedom $\nu > 0$
ncp	Noncentrality parameter $\delta$

Returns: $\Pr[X \leq x]$ where is a noncentral Student's t-distributed random variable with $\nu$ degrees of freedom and noncentrality parameter $\delta$

◆ non_central_t_pdf()

float8 non_central_t_pdf	(	float8	x,
		float8	df,
		float8	ncp
	)

Parameters

x	Random variate
df	Degrees of freedom $\nu > 0$
ncp	Noncentrality parameter $\delta$

Returns: such that $p = \Pr[X \leq x]$ where is a noncentral Student's t-distributed random variable with $\nu$ degrees of freedom and noncentrality parameter $\delta$

◆ non_central_t_quantile()

float8 non_central_t_quantile	(	float8	p,
		float8	df,
		float8	ncp
	)

Parameters

p	Probability $p \in [0,1]$
df	Degrees of freedom $\nu > 0$
ncp	Noncentrality parameter $\delta$

Returns: such that $p = \Pr[X \leq x]$ where is a noncentral Student's t-distributed random variable with $\nu$ degrees of freedom and noncentrality parameter $\delta$

◆ normal_cdf() [1/3]

float8 normal_cdf	(	float8	x,
		float8	mean = `0`,
		float8	sd = `1`
	)

Parameters

x	Random variate
mean	Mean $\mu$
sd	Standard deviation $\sigma > 0$

Returns: $\Pr[X \leq x]$ where is a normally distributed random variable with mean $\mu$ and variance $\sigma^2$

◆ normal_cdf() [2/3]

float8 normal_cdf	(	float8	x,
		float8	mean
	)

◆ normal_cdf() [3/3]

float8 normal_cdf ( float8 x )

◆ normal_pdf() [1/3]

float8 normal_pdf	(	float8	x,
		float8	mean = `0`,
		float8	sd = `1`
	)

Parameters

x	Random variate
mean	Mean $\mu$
sd	Standard deviation $\sigma > 0$

Returns: where is the probability density function of a normally distributed random variable with mean $\mu$ and variance $\sigma^2$

◆ normal_pdf() [2/3]

float8 normal_pdf	(	float8	x,
		float8	mean
	)

◆ normal_pdf() [3/3]

float8 normal_pdf ( float8 x )

◆ normal_quantile() [1/3]

float8 normal_quantile	(	float8	p,
		float8	mean = `0`,
		float8	sd = `1`
	)

Parameters

p	Probability $p \in [0,1]$
mean	Mean $\mu$
sd	Standard deviation $\sigma > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a normally distributed random variable with mean $\mu$ and variance $\sigma^2$

◆ normal_quantile() [2/3]

float8 normal_quantile	(	float8	p,
		float8	mean
	)

◆ normal_quantile() [3/3]

float8 normal_quantile ( float8 p )

◆ pareto_cdf()

float8 pareto_cdf	(	float8	x,
		float8	scale,
		float8	shape
	)

Parameters

x	Random variate
scale	Scale $\beta > 0$
shape	Shape $\alpha > 0$

Returns: $\Pr[X \leq x]$ where is a Pareto-distributed random variable with shape and scale parameters $\alpha$ and $\beta$ , respectively

◆ pareto_pdf()

float8 pareto_pdf	(	float8	x,
		float8	scale,
		float8	shape
	)

Parameters

x	Random variate
scale	Scale $\beta > 0$
shape	Shape $\alpha > 0$

Returns: where is the probability density function of a Pareto-distributed random variable with shape and scale parameters $\alpha$ and $\beta$ , respectively

◆ pareto_quantile()

float8 pareto_quantile	(	float8	p,
		float8	scale,
		float8	shape
	)

Parameters

p	Probability $p \in [0,1]$
scale	Scale $\beta > 0$
shape	Shape $\alpha > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a Pareto-distributed random variable with shape and scale parameters $\alpha$ and $\beta$ , respectively

◆ poisson_cdf()

float8 poisson_cdf	(	float8	x,
		float8	mean
	)

Parameters

x	Random variate
mean	Average occurrence rate $\lambda > 0$

Returns: $\Pr[X \leq x]$ where is a Poisson distributed random variable with mean $\lambda$

◆ poisson_pmf()

float8 poisson_pmf	(	int4	x,
		float8	mean
	)

Parameters

x	Random variate
mean	Average occurrence rate $\lambda > 0$

Returns: where is the probability mass function of a Poisson distributed random variable with mean $\lambda$

◆ poisson_quantile()

float8 poisson_quantile	(	float8	p,
		float8	mean
	)

Parameters

p	Probability $p \in [0,1]$
mean	Average occurrence rate $\lambda > 0$

Returns: If the maximum such that $p \geq \Pr[X \leq x]$ . If $p \geq 0.5$ the minimum such that $p \leq \Pr[X \leq x]$ . Here, is a Poisson distributed random variable with mean $\lambda$

◆ rayleigh_cdf()

float8 rayleigh_cdf	(	float8	x,
		float8	scale
	)

Parameters

x	Random variate
scale	Scale $\sigma > 0$

Returns: $\Pr[X \leq x]$ where is a Rayleigh-distributed random variable with parameter $\sigma$

◆ rayleigh_pdf()

float8 rayleigh_pdf	(	float8	x,
		float8	scale
	)

Parameters

x	Random variate
scale	Scale $\sigma > 0$

Returns: where is the probability density function of a Rayleigh-distributed random variable with parameter $\sigma$

◆ rayleigh_quantile()

float8 rayleigh_quantile	(	float8	p,
		float8	scale
	)

Parameters

p	Probability $p \in [0,1]$
scale	Scale $\sigma > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a Rayleigh-distributed random variable with parameter $\sigma$

◆ students_t_cdf()

float8 students_t_cdf	(	float8	x,
		float8	df
	)

Parameters

x	Random variate
df	Degrees of freedom $\nu > 0$

Returns: $\Pr[X \leq x]$ where is a Student's t-distributed random variable with $\nu$ degrees of freedom

◆ students_t_pdf()

float8 students_t_pdf	(	float8	x,
		float8	df
	)

Parameters

x	Random variate
df	Degrees of freedom $\nu > 0$

Returns: where is the probability density function of a Stundent's t-distributed random variable with $\nu$ degrees of freedom

◆ students_t_quantile()

float8 students_t_quantile	(	float8	p,
		float8	df
	)

Parameters

p	Probability $p \in [0,1]$
df	Degrees of freedom $\nu > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a Student's t-distributed random variable with $\nu$ degrees of freedom

◆ triangular_cdf()

float8 triangular_cdf	(	float8	x,
		float8	lower,
		float8	mode,
		float8	upper
	)

Parameters

x	Random variate
lower	Lower bound
mode	Mode $c \geq a$
upper	Upper bound $b \geq c$ , where

Returns: $\Pr[X \leq x]$ where is a triangular distributed random variable with parameters

◆ triangular_pdf()

float8 triangular_pdf	(	float8	x,
		float8	lower,
		float8	mode,
		float8	upper
	)

Parameters

x	Random variate
lower	Lower bound
mode	Mode $c \geq a$
upper	Upper bound $b \geq c$ , where

Returns: where is the probability density function of a triangular distributed random variable with parameters

◆ triangular_quantile()

float8 triangular_quantile	(	float8	p,
		float8	lower,
		float8	mode,
		float8	upper
	)

Parameters

p	Probability $p \in [0,1]$
lower	Lower bound
mode	Mode $c \geq a$
upper	Upper bound $b \geq c$ , where

Returns: such that $p = \Pr[X \leq x]$ where is a trianbular distributed random variable with parameters

◆ uniform_cdf()

float8 uniform_cdf	(	float8	x,
		float8	lower,
		float8	upper
	)

Parameters

x	Random variate
lower	Lower bound
upper	Upper bound

Returns: $\Pr[X \leq x]$ where is a uniform distributed random variable with support

◆ uniform_pdf()

float8 uniform_pdf	(	float8	x,
		float8	lower,
		float8	upper
	)

Parameters

x	Random variate
lower	Lower bound
upper	Upper bound

Returns: where is the probability density function of a uniform distributed random variable with support

◆ uniform_quantile()

float8 uniform_quantile	(	float8	p,
		float8	lower,
		float8	upper
	)

Parameters

p	Probability $p \in [0,1]$
lower	Lower bound
upper	Upper bound

Returns: such that $p = \Pr[X \leq x]$ where is a uniform distributed random variable with support

◆ weibull_cdf()

float8 weibull_cdf	(	float8	x,
		float8	shape,
		float8	scale
	)

Parameters

x	Random variate
shape	Shape $\alpha > 0$
scale	Scale $\beta > 0$

Returns: $\Pr[X \leq x]$ where is a weibull distributed random variable with shape and scale parameters $\alpha$ and $\beta$ , respectively

◆ weibull_pdf()

float8 weibull_pdf	(	float8	x,
		float8	shape,
		float8	scale
	)

Parameters

x	Random variate
shape	Shape $\alpha > 0$
scale	Scale $\beta > 0$

Returns: where is the probability density function of a weibull distributed random variable with shape and scale parameters $\alpha$ and $\beta$ , respectively

◆ weibull_quantile()

float8 weibull_quantile	(	float8	p,
		float8	shape,
		float8	scale
	)

Parameters

p	Probability $p \in [0,1]$
shape	Shape $\alpha > 0$
scale	Scale $\beta > 0$

Returns: such that $p = \Pr[X \leq x]$ where is a weibull distributed random variable with shape and scale parameters $\alpha$ and $\beta$ , respectively

Functions

Detailed Description

Function Documentation

◆ bernoulli_cdf()

◆ bernoulli_pmf()

◆ bernoulli_quantile()

◆ beta_cdf()

◆ beta_pdf()

◆ beta_quantile()

◆ binomial_cdf()

◆ binomial_pmf()

◆ binomial_quantile()

◆ cauchy_cdf()

◆ cauchy_pdf()

◆ cauchy_quantile()

◆ chi_squared_cdf()

◆ chi_squared_pdf()

◆ chi_squared_quantile()

◆ exponential_cdf()

◆ exponential_pdf()

◆ exponential_quantile()

◆ extreme_value_cdf()

◆ extreme_value_pdf()

◆ extreme_value_quantile()

◆ fisher_f_cdf()

◆ fisher_f_pdf()

◆ fisher_f_quantile()

◆ gamma_cdf()

◆ gamma_pdf()

◆ gamma_quantile()

◆ geometric_cdf()

◆ geometric_pmf()

◆ geometric_quantile()

◆ hypergeometric_cdf()

◆ hypergeometric_pmf()

◆ hypergeometric_quantile()

◆ inverse_gamma_cdf()

◆ inverse_gamma_pdf()

◆ inverse_gamma_quantile()

◆ kolmogorov_cdf()

◆ laplace_cdf()

◆ laplace_pdf()

◆ laplace_quantile()

◆ logistic_cdf()

◆ logistic_pdf()

◆ logistic_quantile()

◆ lognormal_cdf()

◆ lognormal_pdf()

◆ lognormal_quantile()

◆ negative_binomial_cdf()

◆ negative_binomial_pmf()

◆ negative_binomial_quantile()

◆ non_central_beta_cdf()

◆ non_central_beta_pdf()

◆ non_central_beta_quantile()

◆ non_central_chi_squared_cdf()

◆ non_central_chi_squared_pdf()

◆ non_central_chi_squared_quantile()

◆ non_central_f_cdf()

◆ non_central_f_pdf()

◆ non_central_f_quantile()

◆ non_central_t_cdf()

◆ non_central_t_pdf()

◆ non_central_t_quantile()

◆ normal_cdf() [1/3]

◆ normal_cdf() [2/3]

◆ normal_cdf() [3/3]

◆ normal_pdf() [1/3]

◆ normal_pdf() [2/3]

◆ normal_pdf() [3/3]

◆ normal_quantile() [1/3]

◆ normal_quantile() [2/3]

◆ normal_quantile() [3/3]

◆ pareto_cdf()

◆ pareto_pdf()

◆ pareto_quantile()

◆ poisson_cdf()

◆ poisson_pmf()

◆ poisson_quantile()

◆ rayleigh_cdf()