stdlib_stats_distribution_uniform.md

title
stats_distribution_uniform

Statistical Distributions -- Uniform Distribution Module

[TOC]

shuffle - Using Fisher-Yates algorithm to generate a random permutation of a list

Status

Experimental

Description

Applying Fisher-Yates algorithm to generate an unbiased permutation for any list of intrinsic numerical data types.

Syntax

result = [[stdlib_stats_distribution_uniform(module):shuffle(interface)]] ( list )

Class

Function.

Arguments

list: argument has intent(in) and is a rank one array of integer, real, or complex type.

Return value

Return a randomized rank one array of the input type.

Example

{!example/stats_distribution_uniform/example_shuffle.f90!}

rvs_uniform - uniform distribution random variates

Status

Experimental

Description

Without argument the function returns a scalar standard uniformly distributed variate U(0,1) of real type with single precision on [0,1].

With single argument scale of integer type the function returns a scalar uniformly distributed variate of integer type on [0,scale]. This is the standard Rectangular distribution.

With single argument scale of real or complex type the function returns a scalar uniformly distributed variate of real type on [0, scale] or complex type on [(0, 0i), (scale, i(scale))].

With double arguments loc and scale the function returns a scalar uniformly distributed random variates of integer or real type on [loc, loc + scale], or complex type on [(loc, i(loc)), ((loc + scale), i(loc + scale))], dependent of input type.

With triple arguments loc, scale and array_size the function returns a rank one array of uniformly distributed variates of integer, real or complex type with an array size of array_size.

For complex type, the real part and imaginary part are independent of each other.

Note: the algorithm used for generating uniform random variates is fundamentally limited to double precision.

Syntax

result = [[stdlib_stats_distribution_uniform(module):rvs_uniform(interface)]] ([[loc,] scale] [[[,array_size]]])

Class

Elemental function (without the third argument).

Arguments

loc: optional argument has intent(in) and is a scalar of type integer, real or complex.

scale: optional argument has intent(in) and is a scalar of type integer, real or complex.

array_size: optional argument has intent(in) and is a scalar of type integer with default kind.

loc and scale must have the same type and kind when both are present.

Return value

The result is a scalar or a rank one array with size of array_size, of type integer, real or complex depending on the input type.

Example

{!example/stats_distribution_uniform/example_uniform_rvs.f90!}

pdf_uniform - Uniform distribution probability density function

Status

Experimental

Description

The probability density function of the uniform distribution:

f(x) = 0 x < loc or x > loc + scale for all types uniform distributions

For random variable x in [loc, loc + scale]:

f(x) = 1 / (scale + 1); for discrete uniform distribution.

f(x) = 1 / scale; for continuous uniform distribution.

f(x) = 1 / (scale%re * scale%im); for complex uniform distribution.

Syntax

result = [[stdlib_stats_distribution_uniform(module):pdf_uniform(interface)]] (x, loc, scale)

Class

Elemental function.

Arguments

x: has intent(in) and is a scalar of type integer, real or complex.

loc: has intent(in) and is a scalar of type integer, real or complex.

scale: has intent(in) and is a scalar of type integer, real or complex.

All three arguments must have the same type and kind.

Return value

The result is a scalar or an array, with a shape conformable to arguments, of type real.

Example

{!example/stats_distribution_uniform/example_uniform_pdf.f90!}

cdf_uniform - Uniform distribution cumulative distribution function

Status

Experimental

Description

Cumulative distribution function of the uniform distribution:

F(x) = 0 x < loc for all types uniform distributions

F(x) = 1 x > loc + scale for all types uniform distributions

For random variable x in [loc, loc + scale]:

F(x) = (x - loc + 1) / (scale + 1); for discrete uniform distribution.

F(x) = (x - loc) / scale; for continuous uniform distribution.

F(x) = (x%re - loc%re)(x%im - loc%im) / (scale%re * scale%im); for complex uniform distribution.

Syntax

result = [[stdlib_stats_distribution_uniform(module):cdf_uniform(interface)]] (x, loc, scale)

Class

Elemental function.

Arguments

x: has intent(in) and is a scalar of type integer, real or complex.

loc: has intent(in) and is a scalar of type integer, real or complex.

scale: has intent(in) and is a scalar of type integer, real or complex.

All three arguments must have the same type and kind.

Return value

The result is a scalar or an array, with a shape conformable to arguments, of type real.

Example

{!example/stats_distribution_uniform/example_uniform_cdf.f90!}