Moment-Generating Function

Weibull distribution moment-generating function (MGF).

The moment-generating function for a Weibull random variable is

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

Installation

npm install @stdlib/stats-base-dists-weibull-mgf

Usage

var mgf = require( '@stdlib/stats-base-dists-weibull-mgf' );

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

var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var mgf = require( '@stdlib/stats-base-dists-weibull-mgf' );

var opts = {
    'dtype': 'float64'
};
var lambda = uniform( 10, EPS, 10.0, opts );
var k = uniform( 10, EPS, 10.0, opts );
var t = uniform( 10, 0.0, 5.0, opts );

logEachMap( 'x: %0.4f, k: %0.4f, λ: %0.4f, M_X(t;k,λ): %0.4f', t, k, lambda, mgf );

C APIs

Usage

#include "stdlib/stats/base/dists/weibull/mgf.h"

stdlib_base_dists_weibull_mgf( t, k, lambda )

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

double out = stdlib_base_dists_weibull_mgf( 1.0, 1.0, 0.5 );
// returns ~2.0

The function accepts the following arguments:

• t: [in] double input value.
• k: [in] double shape parameter.
• λ: [in] double scale parameter.

double stdlib_base_dists_weibull_mgf( const double t, const double k, const double λ );

Examples

#include "stdlib/stats/base/dists/weibull/mgf.h"
#include "stdlib/constants/float64/eps.h"
#include <stdlib.h>
#include <stdio.h>

static double random_uniform( const double min, const double max ) {
    double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
    return min + ( v*(max-min) );
}

int main( void ) {
    double lambda;
    double k;
    double t;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        t = random_uniform( 0.0, 5.0 );
        k = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        lambda = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
        y = stdlib_base_dists_weibull_mgf( t, k, lambda );
        printf( "t: %lf, k: %lf, λ: %lf, M_X(t;k,λ): %lf\n", t, k, lambda, y );
    }
}

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 © 2016-2026. The Stdlib Authors.