Moment-Generating Function

Beta distribution moment-generating function (MGF).

The moment-generating function for a beta random variable is

where alpha > 0 is the first shape parameter and beta > 0 is the second shape parameter.

Installation

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

Usage

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

mgf( t, alpha, beta )

Evaluates the moment-generating function (MGF) for a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var y = mgf( 0.5, 1.0, 1.0 );
// returns ~1.297

y = mgf( 0.5, 2.0, 4.0 );
// returns ~1.186

y = mgf( 3.0, 2.0, 2.0 );
// returns ~5.575

y = mgf( -0.8, 4.0, 4.0 );
// returns ~0.676

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 alpha <= 0, the function returns NaN.

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

y = mgf( 2.0, 0.0, 0.5 );
// returns NaN

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

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

y = mgf( 2.0, 0.5, 0.0 );
// returns NaN

mgf.factory( alpha, beta )

Returns a function for evaluating the moment-generating function for a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

var mymgf = mgf.factory( 0.5, 0.5 );

var y = mymgf( 0.8 );
// returns ~1.552

y = mymgf( 0.3 );
// returns ~1.168

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-beta-mgf' );

var opts = {
    'dtype': 'float64'
};
var alpha = uniform( 10, EPS, 5.0, opts );
var beta = uniform( 10, EPS, 5.0, opts );
var t = uniform( 10, 0.0, 20.0, opts );

logEachMap( 't: %0.4f, α: %0.4f, β: %0.4f, M_X(t;α,β): %0.4f', t, alpha, beta, mgf );

C APIs

Usage

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

stdlib_base_dists_beta_mgf( t, alpha, beta )

Evaluates the moment-generating function (MGF) for a beta distribution with parameters alpha (first shape parameter) and beta (second shape parameter).

double y = stdlib_base_dists_beta_mgf( 0.5, 1.0, 1.0 );
// returns ~1.297

The function accepts the following arguments:

• t: [in] double input value.
• alpha: [in] double first shape parameter.
• beta: [in] double second shape parameter.

double stdlib_base_dists_beta_mgf( const double t, const double alpha, const double beta );

Examples

#include "stdlib/stats/base/dists/beta/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 alpha;
    double beta;
    double t;
    double y;
    int i;
    for ( i = 0; i < 25; i++ ) {
        t = random_uniform( 0.0, 20.0 );
        alpha = random_uniform( 1.0 + STDLIB_CONSTANT_FLOAT64_EPS, 100.0 );
        beta = random_uniform( 1.0 + STDLIB_CONSTANT_FLOAT64_EPS, 100.0 );
        y = stdlib_base_dists_beta_mgf( alpha, beta );
        printf( "t: %lf, α: %lf, β: %lf, M_X(t;α,β): %lf\n", t, alpha, beta, 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.