About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

Probability Mass Function

Discrete uniform distribution probability mass function (PMF).

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

$$P(X=x;a,b)=\begin{cases} \frac{1}{b - a + 1} & \text{for } x \in \{ a, \ldots, b \} \\ 0 & \text{otherwise} \end{cases}$$

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

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

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

---

Copyright

Copyright © 2016-2024. The Stdlib Authors.