@stdlib/stats-base-dists-negative-binomial-mgf
v0.2.3TypeScript
Negative binomial distribution moment-generating function (MGF).
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Published by The Stdlib Authors
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About stdlib...
Moment-Generating Function
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> [Negative binomial][negative-binomial-distribution] distribution moment-generating function (MGF).
The [moment-generating function][mgf] for a [negative binomial][negative-binomial-distribution] random variable is
where r > 0 is the number of failures until the experiment is stopped and 0 <= p <= 1 is the success probability.
Installation
``bash`
npm install @stdlib/stats-base-dists-negative-binomial-mgf
Usage
`javascript`
var mgf = require( '@stdlib/stats-base-dists-negative-binomial-mgf' );
#### mgf( t, r, p )
Evaluates the [moment-generating function][mgf] for a [negative binomial][negative-binomial-distribution] distribution with number of successes until experiment is stopped r and success probability p.
`javascript
var y = mgf( 0.05, 20.0, 0.8 );
// returns ~267.839
y = mgf( 0.1, 20.0, 0.1 );
// returns ~9.347
`
While r can be interpreted as the number of successes until the experiment is stopped, the [negative binomial][negative-binomial-distribution] distribution is also defined for non-integers r. In this case, r denotes shape parameter of the [gamma mixing distribution][negative-binomial-mixture-representation].
`javascript
var y = mgf( 0.1, 15.5, 0.5 );
// returns ~26.375
y = mgf( 0.5, 7.4, 0.4 );
// returns ~2675.677
`
If t >= -ln( p ), the function returns NaN.
`javascript`
var y = mgf( 0.7, 15.5, 0.5 ); // -ln( p ) = ~0.693
// returns NaN
If provided a r which is not a positive number, the function returns NaN.
`javascript
var y = mgf( 0.2, 0.0, 0.5 );
// returns NaN
y = mgf( 0.2, -2.0, 0.5 );
// returns NaN
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = mgf( NaN, 20.0, 0.5 );
// returns NaN
y = mgf( 0.0, NaN, 0.5 );
// returns NaN
y = mgf( 0.0, 20.0, NaN );
// returns NaN
`
If provided a success probability p outside of [0,1], the function returns NaN.
`javascript
var y = mgf( 0.2, 20, -1.0 );
// returns NaN
y = mgf( 0.2, 20, 1.5 );
// returns NaN
`
#### mgf.factory( r, p )
Returns a function for evaluating the [moment-generating function][mgf] of a [negative binomial][negative-binomial-distribution] distribution with number of successes until experiment is stopped r and success probability p.
`javascript
var myMGF = mgf.factory( 4.3, 0.4 );
var y = myMGF( 0.2 );
// returns ~4.696
y = myMGF( 0.4 );
// returns ~30.83
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var mgf = require( '@stdlib/stats-base-dists-negative-binomial-mgf' );
var opts = {
'dtype': 'float64'
};
var t = uniform( 10, -0.5, 0.5, opts );
var r = uniform( 10, 0.0, 50.0, opts );
var p = uniform( 10, 0.0, 1.0, opts );
logEachMap( 't: %0.4f, r: %0.4f, p: %0.4f, M_X(t;r,p): %0.4f', t, r, p, mgf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/negative-binomial/mgf.h"
#### stdlib_base_dists_negative_binomial_mgf( t, r, p )
Evaluates the [moment-generating function][mgf] for a [negative binomial][negative-binomial-distribution] distribution with number of successes until experiment is stopped r and success probability p.
`c`
double out = stdlib_base_dists_negative_binomial_mgf( 0.05, 20.0, 0.8 );
// returns ~267.839
The function accepts the following arguments:
- t: [in] double input value.[in] double
- r: number of successes until experiment is stopped.[in] double
- p: success probability.
`c`
double stdlib_base_dists_negative_binomial_mgf( const double t, const double r, const double p );
$3
`c
#include "stdlib/stats/base/dists/negative-binomial/mgf.h"
#include
#include
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 t;
double r;
double p;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
t = random_uniform( -1.0, 1.0 );
r = random_uniform( 1.0, 10.0 );
p = random_uniform( 0.0, 1.0 );
y = stdlib_base_dists_negative_binomial_mgf( t, r, p );
printf( "t: %lf, r: %lf, p: %lf, M_X(t;r,p): %lf\n", t, r, p, y );
}
}
`
*
Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
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---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function
[negative-binomial-mixture-representation]: https://en.wikipedia.org/wiki/Negative_binomial_distribution#Gamma.E2.80.93Poisson_mixture
[negative-binomial-distribution]: https://en.wikipedia.org/wiki/Negative_binomial_distribution