README.md

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.

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Moment-Generating Function

Weibull distribution moment-generating function (MGF).

The moment-generating function for a Weibull random variable is

$$M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = \sum_{n=0}^\infty \frac{t^n\lambda^n}{n!}\Gamma\left(1+\frac{n}{k}\right)$$

where lambda > 0 is the scale paramater and k > 0 is the shape parameter.

Usage

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

mgf( t, k, lambda )

Evaluates the moment-generating function (MGF) for a Weibull distribution with shape parameter k and scale parameter lambda.

var y = mgf( 1.0, 1.0, 0.5);
// returns ~2.0

y = mgf( -1.0, 4.0, 4.0 );
// returns ~0.019

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

var y = mgf( NaN, 1.0, 1.0 );
// returns NaN

y = mgf( 0.0, NaN, 1.0 );
// returns NaN

y = mgf( 0.0, 1.0, NaN );
// returns NaN

If provided k <= 0, the function returns NaN.

var y = mgf( 0.2, -1.0, 0.5 );
// returns NaN

y = mgf( 0.2, 0.0, 0.5 );
// returns NaN

If provided lambda <= 0, the function returns NaN.

var y = mgf( 0.2, 0.5, -1.0 );
// returns NaN

y = mgf( 0.2, 0.5, 0.0 );
// returns NaN

mgf.factory( k, lambda )

Returns a function for evaluating the moment-generating function of a Weibull distribution with shape parameter k and scale parameter lambda.

var myMGF = mgf.factory( 8.0, 10.0 );

var y = myMGF( 0.8 );
// returns ~3150.149

y = myMGF( 0.08 );
// returns ~2.137

Examples

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import EPS from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-eps@deno/mod.js';
import mgf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-weibull-mgf@deno/mod.js';

var lambda;
var k;
var t;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    t = randu() * 5.0;
    lambda = ( randu() * 10.0 ) + EPS;
    k = ( randu() * 10.0 ) + EPS;
    y = mgf( t, lambda, k );
    console.log( 'x: %d, k: %d, λ: %d, M_X(t;k,λ): %d', t.toFixed( 4 ), k.toFixed( 4 ), lambda.toFixed( 4 ), y.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.