README.md

About stdlib...

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Moment-Generating Function

Discrete uniform distribution moment-generating function (MGF).

The moment-generating function for a discrete uniform random variable is

$$M_X(t) := \mathbb{E}\!\left[e^{tX}\right]= \begin{cases} \frac{\mathrm{e}^{at}-\mathrm{e}^{t(b+1)}}{(b-a+1)(1-e^t)} & \text{for } t \neq 0 \\ 1 & \text{for } t = 0 \end{cases}$$

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

Usage

import mgf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-discrete-uniform-mgf@deno/mod.js';

You can also import the following named exports from the package:

import { factory } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-discrete-uniform-mgf@deno/mod.js';

mgf( t, a, b )

Evaluates the moment-generating function (MGF) for a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var y = mgf( 2.0, 0, 4 );
// returns ~689.475

y = mgf( -0.2, 0, 4 );
// returns ~0.697

y = mgf( 2.0, 0, 1 );
// returns ~4.195

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

var y = mgf( 0.2, 1, 5.5 );
// returns NaN

If provided a > b, the function returns NaN.

var y = mgf( 0.5, 3, 2);
// returns NaN

If provided NaN for any parameter, the function returns NaN.

var y = mgf( NaN, 0, 1 );
// returns NaN

y = mgf( 0.0, NaN, 1 );
// returns NaN

y = mgf( 0.0, 0, NaN );
// returns NaN

mgf.factory( a, b )

Returns a function for evaluating the moment-generating function (MGF) of a discrete uniform distribution with parameters a (minimum support) and b (maximum support).

var mymgf = mgf.factory( 6, 7 );
var y = mymgf( 0.1 );
// returns ~1.918

y = mymgf( 1.1 );
// returns ~1471.722

Examples

import randint from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-discrete-uniform@deno/mod.js';
import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import mgf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-discrete-uniform-mgf@deno/mod.js';

var randa = randint.factory( 0, 5 );
var randb = randint.factory();
var a;
var b;
var t;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    t = randu();
    a = randa();
    b = randb( a, a+randa() );
    v = mgf( t, a, b );
    console.log( 't: %d, a: %d, b: %d, M_X(t;a,b): %d', t.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}

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Notice

This package is part of stdlib, a standard library 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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.