Moment-Generating Function

Binomial distribution moment-generating function (MGF).

The moment-generating function for a binomial random variable is

where the nonnegative integer n is the number of trials and 0 <= p <= 1 is the success probability.

Installation

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

Usage

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

mgf( t, n, p )

Evaluates the moment-generating function for a binomial distribution with number of trials n and success probability p.

var y = mgf( 0.5, 20, 0.2 );
// returns ~11.471

y = mgf( 5.0, 20, 0.2 );
// returns ~4.798e29

y = mgf( 0.9, 10, 0.4 );
// returns ~99.338

y = mgf( 0.0, 10, 0.4 );
// returns 1.0

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

var y = mgf( NaN, 20, 0.5 );
// returns NaN

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

y = mgf( 0.0, 20, NaN );
// returns NaN

If provided a number of trials n which is not a nonnegative integer, the function returns NaN.

var y = mgf( 0.2, 1.5, 0.5 );
// returns NaN

y = mgf( 0.2, -2.0, 0.5 );
// returns NaN

If provided a success probability p outside of [0,1], the function returns NaN.

var y = mgf( 0.2, 20, -1.0 );
// returns NaN

y = mgf( 0.2, 20, 1.5 );
// returns NaN

mgf.factory( n, p )

Returns a function for evaluating the moment-generating function of a binomial distribution with number of trials n and success probability p.

var myMGF = mgf.factory( 10, 0.5 );

var y = myMGF( 0.3 );
// returns ~5.013

Examples

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

var opts = {
    'dtype': 'float64'
};
var t = discreteUniform( 10, 0, 5, opts );
var n = discreteUniform( 10, 0, 10, opts );
var p = uniform( 10, 0.0, 1.0, opts );

logEachMap( 't: %0.4f, n: %0.4f, p: %0.4f, M_X(t;n,p): %0.4f', t, n, p, mgf );

C APIs

Usage

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

stdlib_base_dists_binomial_mgf( t, n, p )

Evaluates the moment-generating function for a binomial distribution with number of trials n and success probability p.

double out = stdlib_base_dists_binomial_mgf( 0.5, 20, 0.2 );
// returns ~11.471

The function accepts the following arguments:

• t: [in] double input value.
• n: [in] int32_t number of trials.
• p: [in] double success probability.

double stdlib_base_dists_binomial_mgf( const double t, const int32_t n, const double p );

Examples

#include "stdlib/stats/base/dists/binomial/mgf.h"
#include "stdlib/math/base/special/ceil.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 ) {
    int32_t n;
    double p;
    double t;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        n = (int32_t)stdlib_base_ceil( random_uniform( 0, 100 ) );
        p = random_uniform( 0, 1 );
        t = random_uniform( 0, 5 );
        y = stdlib_base_dists_binomial_mgf( t, n, p );
        printf( "t: %lf, n: %d, p: %lf, M_X(t;n,p): %lf\n", t, n, p, y );
    }

    return 0;
}

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.