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---
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
```fortran
{!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
```fortran
{!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
```fortran
{!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
```fortran
{!example/stats_distribution_uniform/example_uniform_cdf.f90!}
```
|
