# @stdlib/stats-base-dists-discrete-uniform-pmf 0.1.0 • Public • Published

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# Probability Mass Function

Discrete uniform distribution probability mass function (PMF).

The probability mass function (PMF) for a discrete uniform random variable is

where `a` is the minimum support and `b` is the maximum support of the distribution. The parameters must satisfy `a <= b`.

## Installation

`npm install @stdlib/stats-base-dists-discrete-uniform-pmf`

## Usage

`var pmf = require( '@stdlib/stats-base-dists-discrete-uniform-pmf' );`

#### pmf( x, a, b )

Evaluates the probability mass function (PMF) for a discrete uniform distribution with parameters `a` (minimum support) and `b` (maximum support).

```var y = pmf( 2.0, 0, 4 );
// returns ~0.2

y = pmf( 5.0, 0, 4 );
// returns 0.0

y = pmf( 3, -4, 4 );
// returns ~0.111```

If provided `NaN` as any argument, the function returns `NaN`.

```var y = pmf( NaN, -2, 2 );
// returns NaN

y = pmf( 1.0, NaN, 4 );
// returns NaN

y = pmf( 2.0, 0, NaN );
// returns NaN```

If `a` or `b` is not an integer value, the function returns `NaN`.

```var y = pmf( 2.0, 1, 5.5 );
// returns NaN```

If provided `a > b`, the function returns `NaN`.

```var y = pmf( 2.0, 3, 2 );
// returns NaN```

#### pmf.factory( a, b )

Returns a `function` for evaluating the PMF for a discrete uniform distribution with parameters `a` (minimum support) and `b` (maximum support).

```var myPDF = pmf.factory( 6, 7 );
var y = myPDF( 7.0 );
// returns 0.5

y = myPDF( 5.0 );
// returns 0.0```

## Examples

```var randint = require( '@stdlib/random-base-discrete-uniform' );
var pmf = require( '@stdlib/stats-base-dists-discrete-uniform-pmf' );

var randa = randint.factory( 0, 10 );
var randb = randint.factory();
var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 25; i++ ) {
a = randa();
x = randb( a, a+randa() );
b = randb( a, a+randa() );
y = pmf( x, a, b );
console.log( 'x: %d, a: %d, b: %d, P(X=x;a,b): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), y.toFixed( 4 ) );
}```

## Notice

This package is part of stdlib, a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.

For more information on the project, filing bug reports and feature requests, and guidance on how to develop stdlib, see the main project repository.

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