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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.