protocol

`univariate_distributions_protocol`

Univariate probability distribution predicates.

Availability:

logtalk_load(univariate_distributions(loader))

Author: Paulo Moura
Version: 1:0:0
Date: 2026-08-12

Compilation flags:

static

Dependencies:

(none)

Remarks:

(none)

Inherited public predicates:

(none)

Public predicates 

`standard_normal/1`

Returns a standard normally distributed random value.

Compilation flags:

static

Template:

standard_normal(Value)

Mode and number of proofs:

standard_normal(-float) - one

`standard_normal_samples/2`

Returns the requested number of standard normally distributed random values.

Compilation flags:

static

Template:

standard_normal_samples(Count,Samples)

Mode and number of proofs:

standard_normal_samples(+integer,-list(float)) - one_or_error

Exceptions:

Count is a variable:

instantiation_error

Count is neither a variable nor an integer:

type_error(integer,Count)

Count is an integer but not a non-negative integer:

domain_error(non_negative_integer,Count)

`normal/3`

Returns a normally distributed random value with the given mean and standard deviation. A zero deviation returns the mean.

Compilation flags:

static

Template:

normal(Mean,Deviation,Value)

Mode and number of proofs:

normal(+float,+non_negative_float,-float) - one_or_error

Exceptions:

Mean is a variable:

instantiation_error

Mean is neither a variable nor a float:

type_error(float,Mean)

Deviation is a variable:

instantiation_error

Deviation is neither a variable nor a float:

type_error(float,Deviation)

Deviation is a negative float:

domain_error(non_negative_float,Deviation)

`normal_samples/4`

Returns the requested number of normally distributed random values with the given mean and standard deviation.

Compilation flags:

static

Template:

normal_samples(Count,Mean,Deviation,Samples)

Mode and number of proofs:

normal_samples(+integer,+float,+non_negative_float,-list(float)) - one_or_error

Exceptions:

Count is a variable:

instantiation_error

Count is neither a variable nor an integer:

type_error(integer,Count)

Count is an integer but not a non-negative integer:

domain_error(non_negative_integer,Count)

Mean is a variable:

instantiation_error

Mean is neither a variable nor a float:

type_error(float,Mean)

Deviation is a variable:

instantiation_error

Deviation is neither a variable nor a float:

type_error(float,Deviation)

Deviation is a negative float:

domain_error(non_negative_float,Deviation)

`standard_normal_density/2`

Computes the standard normal probability density at the given value.

Compilation flags:

static

Template:

standard_normal_density(Value,Density)

Mode and number of proofs:

standard_normal_density(+number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

`standard_normal_log_density/2`

Computes the standard normal log-density at the given value.

Compilation flags:

static

Template:

standard_normal_log_density(Value,LogDensity)

Mode and number of proofs:

standard_normal_log_density(+number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

`standard_normal_distribution/2`

Computes an approximation of the standard normal cumulative distribution at the given value.

Compilation flags:

static

Template:

standard_normal_distribution(Value,Probability)

Mode and number of proofs:

standard_normal_distribution(+number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

`standard_normal_quantile/2`

Computes an approximation of the standard normal quantile for a probability strictly between zero and one.

Compilation flags:

static

Template:

standard_normal_quantile(Probability,Quantile)

Mode and number of proofs:

standard_normal_quantile(+open_probability,-float) - one_or_error

Exceptions:

Probability is a variable:

instantiation_error

Probability is neither a variable nor a float:

type_error(float,Probability)

Probability is a float but not strictly between zero and one:

domain_error(open_probability,Probability)

`normal_density/4`

Computes the normal probability density at a value for the given mean and positive standard deviation.

Compilation flags:

static

Template:

normal_density(Value,Mean,Deviation,Density)

Mode and number of proofs:

normal_density(+number,+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Mean is a variable:

instantiation_error

Mean is neither a variable nor a number:

type_error(number,Mean)

Deviation is a variable:

instantiation_error

Deviation is neither a variable nor a number:

type_error(number,Deviation)

Deviation is a number but not a positive number:

domain_error(positive_number,Deviation)

`normal_log_density/4`

Computes the normal log-density at a value for the given mean and positive standard deviation.

Compilation flags:

static

Template:

normal_log_density(Value,Mean,Deviation,LogDensity)

Mode and number of proofs:

normal_log_density(+number,+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Mean is a variable:

instantiation_error

Mean is neither a variable nor a number:

type_error(number,Mean)

Deviation is a variable:

instantiation_error

Deviation is neither a variable nor a number:

type_error(number,Deviation)

Deviation is a number but not a positive number:

domain_error(positive_number,Deviation)

`normal_distribution/4`

Computes an approximation of the normal cumulative distribution at a value for the given mean and positive standard deviation.

Compilation flags:

static

Template:

normal_distribution(Value,Mean,Deviation,Probability)

Mode and number of proofs:

normal_distribution(+number,+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Mean is a variable:

instantiation_error

Mean is neither a variable nor a number:

type_error(number,Mean)

Deviation is a variable:

instantiation_error

Deviation is neither a variable nor a number:

type_error(number,Deviation)

Deviation is a number but not a positive number:

domain_error(positive_number,Deviation)

`normal_quantile/4`

Computes an approximation of the normal quantile for a probability strictly between zero and one and the given mean and positive standard deviation.

Compilation flags:

static

Template:

normal_quantile(Probability,Mean,Deviation,Quantile)

Mode and number of proofs:

normal_quantile(+open_probability,+number,+positive_number,-float) - one_or_error

Exceptions:

Probability is a variable:

instantiation_error

Probability is neither a variable nor a float:

type_error(float,Probability)

Probability is a float but not strictly between zero and one:

domain_error(open_probability,Probability)

Mean is a variable:

instantiation_error

Mean is neither a variable nor a number:

type_error(number,Mean)

Deviation is a variable:

instantiation_error

Deviation is neither a variable nor a number:

type_error(number,Deviation)

Deviation is a number but not a positive number:

domain_error(positive_number,Deviation)

`standard_t/2`

Returns a standard Student’s t distributed random value.

Compilation flags:

static

Template:

standard_t(DegreesOfFreedom,Value)

Mode and number of proofs:

standard_t(+positive_number,-float) - one_or_error

Exceptions:

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`standard_t_samples/3`

Returns the requested number of standard Student’s t distributed random values.

Compilation flags:

static

Template:

standard_t_samples(Count,DegreesOfFreedom,Samples)

Mode and number of proofs:

standard_t_samples(+integer,+positive_number,-list(float)) - one_or_error

Exceptions:

Count is a variable:

instantiation_error

Count is neither a variable nor an integer:

type_error(integer,Count)

Count is an integer but not a non-negative integer:

domain_error(non_negative_integer,Count)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`standard_t_density/3`

Computes the standard Student’s t probability density at the given value.

Compilation flags:

static

Template:

standard_t_density(Value,DegreesOfFreedom,Density)

Mode and number of proofs:

standard_t_density(+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`standard_t_log_density/3`

Computes the standard Student’s t log-density at the given value.

Compilation flags:

static

Template:

standard_t_log_density(Value,DegreesOfFreedom,LogDensity)

Mode and number of proofs:

standard_t_log_density(+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`standard_t_distribution/3`

Computes an approximation of the standard Student’s t cumulative distribution at the given value.

Compilation flags:

static

Template:

standard_t_distribution(Value,DegreesOfFreedom,Probability)

Mode and number of proofs:

standard_t_distribution(+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`standard_t_quantile/3`

Computes an approximation of the standard Student’s t quantile for a probability strictly between zero and one.

Compilation flags:

static

Template:

standard_t_quantile(Probability,DegreesOfFreedom,Quantile)

Mode and number of proofs:

standard_t_quantile(+open_probability,+positive_number,-float) - one_or_error

Exceptions:

Probability is a variable:

instantiation_error

Probability is neither a variable nor a float:

type_error(float,Probability)

Probability is a float but not strictly between zero and one:

domain_error(open_probability,Probability)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`t/4`

Returns a location-scale Student’s t distributed random value.

Compilation flags:

static

Template:

t(Location,Scale,DegreesOfFreedom,Value)

Mode and number of proofs:

t(+number,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Location is a variable:

instantiation_error

Location is neither a variable nor a number:

type_error(number,Location)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`t_samples/5`

Returns the requested number of location-scale Student’s t distributed random values.

Compilation flags:

static

Template:

t_samples(Count,Location,Scale,DegreesOfFreedom,Samples)

Mode and number of proofs:

t_samples(+integer,+number,+positive_number,+positive_number,-list(float)) - one_or_error

Exceptions:

Count is a variable:

instantiation_error

Count is neither a variable nor an integer:

type_error(integer,Count)

Count is an integer but not a non-negative integer:

domain_error(non_negative_integer,Count)

Location is a variable:

instantiation_error

Location is neither a variable nor a number:

type_error(number,Location)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`t_density/5`

Computes the location-scale Student’s t probability density.

Compilation flags:

static

Template:

t_density(Value,Location,Scale,DegreesOfFreedom,Density)

Mode and number of proofs:

t_density(+number,+number,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Location is a variable:

instantiation_error

Location is neither a variable nor a number:

type_error(number,Location)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`t_log_density/5`

Computes the location-scale Student’s t log-density.

Compilation flags:

static

Template:

t_log_density(Value,Location,Scale,DegreesOfFreedom,LogDensity)

Mode and number of proofs:

t_log_density(+number,+number,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Location is a variable:

instantiation_error

Location is neither a variable nor a number:

type_error(number,Location)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`t_distribution/5`

Computes an approximation of the location-scale Student’s t cumulative distribution.

Compilation flags:

static

Template:

t_distribution(Value,Location,Scale,DegreesOfFreedom,Probability)

Mode and number of proofs:

t_distribution(+number,+number,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Location is a variable:

instantiation_error

Location is neither a variable nor a number:

type_error(number,Location)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`t_quantile/5`

Computes an approximation of the location-scale Student’s t quantile for a probability strictly between zero and one.

Compilation flags:

static

Template:

t_quantile(Probability,Location,Scale,DegreesOfFreedom,Quantile)

Mode and number of proofs:

t_quantile(+open_probability,+number,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Probability is a variable:

instantiation_error

Probability is neither a variable nor a float:

type_error(float,Probability)

Probability is a float but not strictly between zero and one:

domain_error(open_probability,Probability)

Location is a variable:

instantiation_error

Location is neither a variable nor a number:

type_error(number,Location)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`chi_squared/2`

Returns a chi-squared distributed random value.

Compilation flags:

static

Template:

chi_squared(DegreesOfFreedom,Value)

Mode and number of proofs:

chi_squared(+positive_number,-float) - one_or_error

Exceptions:

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`chi_squared_samples/3`

Returns the requested number of chi-squared distributed random values.

Compilation flags:

static

Template:

chi_squared_samples(Count,DegreesOfFreedom,Samples)

Mode and number of proofs:

chi_squared_samples(+integer,+positive_number,-list(float)) - one_or_error

Exceptions:

Count is a variable:

instantiation_error

Count is neither a variable nor an integer:

type_error(integer,Count)

Count is an integer but not a non-negative integer:

domain_error(non_negative_integer,Count)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`chi_squared_density/3`

Computes the chi-squared probability density at the given value. At zero, returns the atom positive_infinity when the degrees of freedom are smaller than two.

Compilation flags:

static

Template:

chi_squared_density(Value,DegreesOfFreedom,Density)

Mode and number of proofs:

chi_squared_density(+number,+positive_number,-atomic) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`chi_squared_log_density/3`

Computes the chi-squared log-density at the given value. Returns the atoms positive_infinity or negative_infinity when the density is respectively infinite or zero.

Compilation flags:

static

Template:

chi_squared_log_density(Value,DegreesOfFreedom,LogDensity)

Mode and number of proofs:

chi_squared_log_density(+number,+positive_number,-atomic) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`chi_squared_distribution/3`

Computes an approximation of the chi-squared cumulative distribution at the given value.

Compilation flags:

static

Template:

chi_squared_distribution(Value,DegreesOfFreedom,Probability)

Mode and number of proofs:

chi_squared_distribution(+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`chi_squared_quantile/3`

Computes an approximation of the chi-squared quantile for a probability strictly between zero and one.

Compilation flags:

static

Template:

chi_squared_quantile(Probability,DegreesOfFreedom,Quantile)

Mode and number of proofs:

chi_squared_quantile(+open_probability,+positive_number,-float) - one_or_error

Exceptions:

Probability is a variable:

instantiation_error

Probability is neither a variable nor a float:

type_error(float,Probability)

Probability is a float but not strictly between zero and one:

domain_error(open_probability,Probability)

DegreesOfFreedom is a variable:

instantiation_error

DegreesOfFreedom is neither a variable nor a number:

type_error(number,DegreesOfFreedom)

DegreesOfFreedom is a number but not a positive number:

domain_error(positive_number,DegreesOfFreedom)

`gamma/3`

Returns a gamma distributed random value (shape-scale parameterization).

Compilation flags:

static

Template:

gamma(Shape,Scale,Value)

Mode and number of proofs:

gamma(+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Shape is a variable:

instantiation_error

Shape is neither a variable nor a number:

type_error(number,Shape)

Shape is not positive:

domain_error(positive_number,Shape)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`gamma_samples/4`

Returns the requested number of gamma distributed random values.

Compilation flags:

static

Template:

gamma_samples(Count,Shape,Scale,Samples)

Mode and number of proofs:

gamma_samples(+integer,+positive_number,+positive_number,-list(float)) - one_or_error

Exceptions:

Count is a variable:

instantiation_error

Count is neither a variable nor an integer:

type_error(integer,Count)

Count is an integer but not a non-negative integer:

domain_error(non_negative_integer,Count)

Shape is a variable:

instantiation_error

Shape is neither a variable nor a number:

type_error(number,Shape)

Shape is not positive:

domain_error(positive_number,Shape)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`gamma_density/4`

Computes the gamma probability density at the given value. At zero, returns the atom positive_infinity when the shape is smaller than one.

Compilation flags:

static

Template:

gamma_density(Value,Shape,Scale,Density)

Mode and number of proofs:

gamma_density(+number,+positive_number,+positive_number,-atomic) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Shape is a variable:

instantiation_error

Shape is neither a variable nor a number:

type_error(number,Shape)

Shape is not positive:

domain_error(positive_number,Shape)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`gamma_log_density/4`

Computes the gamma log-density at the given value. Returns the atoms positive_infinity or negative_infinity when the density is respectively infinite or zero.

Compilation flags:

static

Template:

gamma_log_density(Value,Shape,Scale,LogDensity)

Mode and number of proofs:

gamma_log_density(+number,+positive_number,+positive_number,-atomic) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Shape is a variable:

instantiation_error

Shape is neither a variable nor a number:

type_error(number,Shape)

Shape is not positive:

domain_error(positive_number,Shape)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`gamma_distribution/4`

Computes an approximation of the gamma cumulative distribution at the given value.

Compilation flags:

static

Template:

gamma_distribution(Value,Shape,Scale,Probability)

Mode and number of proofs:

gamma_distribution(+number,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Shape is a variable:

instantiation_error

Shape is neither a variable nor a number:

type_error(number,Shape)

Shape is not positive:

domain_error(positive_number,Shape)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`gamma_quantile/4`

Computes an approximation of the gamma quantile for a probability strictly between zero and one.

Compilation flags:

static

Template:

gamma_quantile(Probability,Shape,Scale,Quantile)

Mode and number of proofs:

gamma_quantile(+open_probability,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Probability is a variable:

instantiation_error

Probability is neither a variable nor a float:

type_error(float,Probability)

Probability is a float but not strictly between zero and one:

domain_error(open_probability,Probability)

Shape is a variable:

instantiation_error

Shape is neither a variable nor a number:

type_error(number,Shape)

Shape is not positive:

domain_error(positive_number,Shape)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`beta/3`

Returns a beta distributed random value.

Compilation flags:

static

Template:

beta(Alpha,Beta,Value)

Mode and number of proofs:

beta(+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Alpha is a variable:

instantiation_error

Alpha is neither a variable nor a number:

type_error(number,Alpha)

Alpha is not positive:

domain_error(positive_number,Alpha)

Beta is a variable:

instantiation_error

Beta is neither a variable nor a number:

type_error(number,Beta)

Beta is not positive:

domain_error(positive_number,Beta)

`beta_samples/4`

Returns the requested number of beta distributed random values.

Compilation flags:

static

Template:

beta_samples(Count,Alpha,Beta,Samples)

Mode and number of proofs:

beta_samples(+integer,+positive_number,+positive_number,-list(float)) - one_or_error

Exceptions:

Count is a variable:

instantiation_error

Count is neither a variable nor an integer:

type_error(integer,Count)

Count is an integer but not a non-negative integer:

domain_error(non_negative_integer,Count)

Alpha is a variable:

instantiation_error

Alpha is neither a variable nor a number:

type_error(number,Alpha)

Alpha is not positive:

domain_error(positive_number,Alpha)

Beta is a variable:

instantiation_error

Beta is neither a variable nor a number:

type_error(number,Beta)

Beta is not positive:

domain_error(positive_number,Beta)

`beta_density/4`

Computes the beta probability density at the given value. At either endpoint, returns the atom positive_infinity when the corresponding shape parameter is smaller than one.

Compilation flags:

static

Template:

beta_density(Value,Alpha,Beta,Density)

Mode and number of proofs:

beta_density(+number,+positive_number,+positive_number,-atomic) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Alpha is a variable:

instantiation_error

Alpha is neither a variable nor a number:

type_error(number,Alpha)

Alpha is not positive:

domain_error(positive_number,Alpha)

Beta is a variable:

instantiation_error

Beta is neither a variable nor a number:

type_error(number,Beta)

Beta is not positive:

domain_error(positive_number,Beta)

`beta_log_density/4`

Computes the beta log-density at the given value. Returns the atoms positive_infinity or negative_infinity when the density is respectively infinite or zero.

Compilation flags:

static

Template:

beta_log_density(Value,Alpha,Beta,LogDensity)

Mode and number of proofs:

beta_log_density(+number,+positive_number,+positive_number,-atomic) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Alpha is a variable:

instantiation_error

Alpha is neither a variable nor a number:

type_error(number,Alpha)

Alpha is not positive:

domain_error(positive_number,Alpha)

Beta is a variable:

instantiation_error

Beta is neither a variable nor a number:

type_error(number,Beta)

Beta is not positive:

domain_error(positive_number,Beta)

`beta_distribution/4`

Computes an approximation of the beta cumulative distribution at the given value.

Compilation flags:

static

Template:

beta_distribution(Value,Alpha,Beta,Probability)

Mode and number of proofs:

beta_distribution(+number,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Alpha is a variable:

instantiation_error

Alpha is neither a variable nor a number:

type_error(number,Alpha)

Alpha is not positive:

domain_error(positive_number,Alpha)

Beta is a variable:

instantiation_error

Beta is neither a variable nor a number:

type_error(number,Beta)

Beta is not positive:

domain_error(positive_number,Beta)

`beta_quantile/4`

Computes an approximation of the beta quantile for a probability strictly between zero and one.

Compilation flags:

static

Template:

beta_quantile(Probability,Alpha,Beta,Quantile)

Mode and number of proofs:

beta_quantile(+open_probability,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Probability is a variable:

instantiation_error

Probability is neither a variable nor a float:

type_error(float,Probability)

Probability is a float but not strictly between zero and one:

domain_error(open_probability,Probability)

Alpha is a variable:

instantiation_error

Alpha is neither a variable nor a number:

type_error(number,Alpha)

Alpha is not positive:

domain_error(positive_number,Alpha)

Beta is a variable:

instantiation_error

Beta is neither a variable nor a number:

type_error(number,Beta)

Beta is not positive:

domain_error(positive_number,Beta)

`exponential/2`

Returns an exponentially distributed random value (scale parameterization).

Compilation flags:

static

Template:

exponential(Scale,Value)

Mode and number of proofs:

exponential(+positive_number,-float) - one_or_error

Exceptions:

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`exponential_samples/3`

Returns the requested number of exponentially distributed random values.

Compilation flags:

static

Template:

exponential_samples(Count,Scale,Samples)

Mode and number of proofs:

exponential_samples(+integer,+positive_number,-list(float)) - one_or_error

Exceptions:

Count is a variable:

instantiation_error

Count is neither a variable nor an integer:

type_error(integer,Count)

Count is an integer but not a non-negative integer:

domain_error(non_negative_integer,Count)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`exponential_density/3`

Computes the exponential probability density at the given value.

Compilation flags:

static

Template:

exponential_density(Value,Scale,Density)

Mode and number of proofs:

exponential_density(+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`exponential_log_density/3`

Computes the exponential log-density at the given value.

Compilation flags:

static

Template:

exponential_log_density(Value,Scale,LogDensity)

Mode and number of proofs:

exponential_log_density(+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`exponential_distribution/3`

Computes the exponential cumulative distribution at the given value.

Compilation flags:

static

Template:

exponential_distribution(Value,Scale,Probability)

Mode and number of proofs:

exponential_distribution(+number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`exponential_quantile/3`

Computes the exponential quantile for a probability strictly between zero and one.

Compilation flags:

static

Template:

exponential_quantile(Probability,Scale,Quantile)

Mode and number of proofs:

exponential_quantile(+open_probability,+positive_number,-float) - one_or_error

Exceptions:

Probability is a variable:

instantiation_error

Probability is neither a variable nor a float:

type_error(float,Probability)

Probability is a float but not strictly between zero and one:

domain_error(open_probability,Probability)

Scale is a variable:

instantiation_error

Scale is neither a variable nor a number:

type_error(number,Scale)

Scale is not positive:

domain_error(positive_number,Scale)

`fisher/3`

Returns a Fisher-Snedecor (F) distributed random value.

Compilation flags:

static

Template:

fisher(DegreesOfFreedom1,DegreesOfFreedom2,Value)

Mode and number of proofs:

fisher(+positive_number,+positive_number,-float) - one_or_error

Exceptions:

DegreesOfFreedom1 is a variable:

instantiation_error

DegreesOfFreedom1 is neither a variable nor a number:

type_error(number,DegreesOfFreedom1)

DegreesOfFreedom1 is not positive:

domain_error(positive_number,DegreesOfFreedom1)

DegreesOfFreedom2 is a variable:

instantiation_error

DegreesOfFreedom2 is neither a variable nor a number:

type_error(number,DegreesOfFreedom2)

DegreesOfFreedom2 is not positive:

domain_error(positive_number,DegreesOfFreedom2)

`fisher_samples/4`

Returns the requested number of Fisher-Snedecor (F) distributed random values.

Compilation flags:

static

Template:

fisher_samples(Count,DegreesOfFreedom1,DegreesOfFreedom2,Samples)

Mode and number of proofs:

fisher_samples(+integer,+positive_number,+positive_number,-list(float)) - one_or_error

Exceptions:

Count is a variable:

instantiation_error

Count is neither a variable nor an integer:

type_error(integer,Count)

Count is an integer but not a non-negative integer:

domain_error(non_negative_integer,Count)

DegreesOfFreedom1 is a variable:

instantiation_error

DegreesOfFreedom1 is neither a variable nor a number:

type_error(number,DegreesOfFreedom1)

DegreesOfFreedom1 is not positive:

domain_error(positive_number,DegreesOfFreedom1)

DegreesOfFreedom2 is a variable:

instantiation_error

DegreesOfFreedom2 is neither a variable nor a number:

type_error(number,DegreesOfFreedom2)

DegreesOfFreedom2 is not positive:

domain_error(positive_number,DegreesOfFreedom2)

`fisher_density/4`

Computes the Fisher-Snedecor (F) probability density at the given value. At zero, returns the atom positive_infinity when the first degrees of freedom are smaller than two.

Compilation flags:

static

Template:

fisher_density(Value,DegreesOfFreedom1,DegreesOfFreedom2,Density)

Mode and number of proofs:

fisher_density(+number,+positive_number,+positive_number,-atomic) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

DegreesOfFreedom1 is a variable:

instantiation_error

DegreesOfFreedom1 is neither a variable nor a number:

type_error(number,DegreesOfFreedom1)

DegreesOfFreedom1 is not positive:

domain_error(positive_number,DegreesOfFreedom1)

DegreesOfFreedom2 is a variable:

instantiation_error

DegreesOfFreedom2 is neither a variable nor a number:

type_error(number,DegreesOfFreedom2)

DegreesOfFreedom2 is not positive:

domain_error(positive_number,DegreesOfFreedom2)

`fisher_log_density/4`

Computes the Fisher-Snedecor (F) log-density at the given value. Returns the atoms positive_infinity or negative_infinity when the density is respectively infinite or zero.

Compilation flags:

static

Template:

fisher_log_density(Value,DegreesOfFreedom1,DegreesOfFreedom2,LogDensity)

Mode and number of proofs:

fisher_log_density(+number,+positive_number,+positive_number,-atomic) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

DegreesOfFreedom1 is a variable:

instantiation_error

DegreesOfFreedom1 is neither a variable nor a number:

type_error(number,DegreesOfFreedom1)

DegreesOfFreedom1 is not positive:

domain_error(positive_number,DegreesOfFreedom1)

DegreesOfFreedom2 is a variable:

instantiation_error

DegreesOfFreedom2 is neither a variable nor a number:

type_error(number,DegreesOfFreedom2)

DegreesOfFreedom2 is not positive:

domain_error(positive_number,DegreesOfFreedom2)

`fisher_distribution/4`

Computes an approximation of the Fisher-Snedecor (F) cumulative distribution at the given value.

Compilation flags:

static

Template:

fisher_distribution(Value,DegreesOfFreedom1,DegreesOfFreedom2,Probability)

Mode and number of proofs:

fisher_distribution(+number,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Value is a variable:

instantiation_error

Value is neither a variable nor a number:

type_error(number,Value)

DegreesOfFreedom1 is a variable:

instantiation_error

DegreesOfFreedom1 is neither a variable nor a number:

type_error(number,DegreesOfFreedom1)

DegreesOfFreedom1 is not positive:

domain_error(positive_number,DegreesOfFreedom1)

DegreesOfFreedom2 is a variable:

instantiation_error

DegreesOfFreedom2 is neither a variable nor a number:

type_error(number,DegreesOfFreedom2)

DegreesOfFreedom2 is not positive:

domain_error(positive_number,DegreesOfFreedom2)

`fisher_quantile/4`

Computes an approximation of the Fisher-Snedecor (F) quantile for a probability strictly between zero and one.

Compilation flags:

static

Template:

fisher_quantile(Probability,DegreesOfFreedom1,DegreesOfFreedom2,Quantile)

Mode and number of proofs:

fisher_quantile(+open_probability,+positive_number,+positive_number,-float) - one_or_error

Exceptions:

Probability is a variable:

instantiation_error

Probability is neither a variable nor a float:

type_error(float,Probability)

Probability is a float but not strictly between zero and one:

domain_error(open_probability,Probability)

DegreesOfFreedom1 is a variable:

instantiation_error

DegreesOfFreedom1 is neither a variable nor a number:

type_error(number,DegreesOfFreedom1)

DegreesOfFreedom1 is not positive:

domain_error(positive_number,DegreesOfFreedom1)

DegreesOfFreedom2 is a variable:

instantiation_error

DegreesOfFreedom2 is neither a variable nor a number:

type_error(number,DegreesOfFreedom2)

DegreesOfFreedom2 is not positive:

domain_error(positive_number,DegreesOfFreedom2)

univariate_distributions_protocol

`univariate_distributions_protocol`