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Degenerate distribution moment-generating function (MGF).
The moment-generating function for a degenerate random variable is
where mu is the distribution mean.
npm install @stdlib/stats-base-dists-degenerate-mgfAlternatively,
- To load the package in a website via a
scripttag without installation and bundlers, use the ES Module available on theesmbranch (see README). - If you are using Deno, visit the
denobranch (see README for usage intructions). - For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the
umdbranch (see README).
The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
var mgf = require( '@stdlib/stats-base-dists-degenerate-mgf' );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 ~403.429If provided NaN for any argument, the function returns NaN.
var y = mgf( NaN, 0.0 );
// returns NaN
y = mgf( 0.0, NaN );
// returns NaNReturns 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 ~2.718var randu = require( '@stdlib/random-base-randu' );
var round = require( '@stdlib/math-base-special-round' );
var mgf = require( '@stdlib/stats-base-dists-degenerate-mgf' );
var mu;
var t;
var y;
var i;
for ( i = 0; i < 100; i++ ) {
t = round( randu()*5.0 );
mu = round( randu()*5.0 );
y = mgf( t, mu );
console.log( 'x: %d, µ: %d, M_X(t;µ): %d', t, mu, y );
}#include "stdlib/stats/base/dists/degenerate/mgf.h"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 ~2.718The function accepts the following arguments:
- t:
[in] doubleinput value. - mu:
[in] doublevalue at which to center the distribution.
double stdlib_base_dists_degenerate_mgf( const double t, const double mu );#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 );
}
}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.
See LICENSE.
Copyright © 2016-2025. The Stdlib Authors.
