Moment-Generating Function

Degenerate distribution moment-generating function (MGF).

The moment-generating function for a degenerate random variable is

where mu is the distribution mean.

Installation

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

Usage

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

mgf( t, mu )

Evaluates the moment-generating function (MGF) of a degenerate distribution with parameter mu (mean).

var y = mgf( 1.0, 1.0 );
// returns ~2.718

y = mgf( 2.0, 3.0 );
// returns ~403.429

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

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

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

mgf.factory( mu )

Returns a function for evaluating the moment-generating function of a degenerate distribution with parameter mu (mean).

var mymgf = mgf.factory( 10.0 );

var y = mymgf( 0.1 );
// returns ~2.718

Examples

var discreteUniform = require( '@stdlib/random-array-discrete-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var mgf = require( '@stdlib/stats-base-dists-degenerate-mgf' );

var opts = {
    'dtype': 'float64'
};
var t = discreteUniform( 100, 0, 5, opts );
var mu = discreteUniform( 100, 0, 5, opts );

logEachMap( 'x: %0.4f, µ: %0.4f, M_X(t;µ): %0.4f', t, mu, mgf );

C APIs

Usage

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

stdlib_base_dists_degenerate_mgf( t, mu )

Evaluates the moment-generating function (MGF) of a degenerate distribution with parameter mu (mean).

double out = stdlib_base_dists_degenerate_mgf( 1.0, 1.0 );
// returns ~2.718

The function accepts the following arguments:

• t: [in] double input value.
• mu: [in] double value at which to center the distribution.

double stdlib_base_dists_degenerate_mgf( const double t, const double mu );

Examples

#include "stdlib/stats/base/dists/degenerate/mgf.h"
#include "stdlib/math/base/special/round.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 result;
    double mu;
    double t;
    int i;

    for ( i = 0; i < 10; i++ ) {
        t = stdlib_base_round( random_uniform( 0.0, 5.0 ) );
        mu = stdlib_base_round( random_uniform( 0.0, 5.0 ) );
        result = stdlib_base_dists_degenerate_mgf( t, mu );
        printf( "t: %lf, µ: %lf, M_X(t;µ): %lf\n", t, mu, result );
    }
}

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.