@stdlib/stats-base-dists-discrete-uniform-mgf
v0.3.1TypeScript
Discrete uniform 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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> [Discrete uniform][discrete-uniform-distribution] distribution moment-generating function (MGF).
The [moment-generating function][mgf] for a [discrete uniform][discrete-uniform-distribution] random variable is
where a is the minimum support and b is the maximum support. The parameters must satisfy a <= b.
Installation
``bash`
npm install @stdlib/stats-base-dists-discrete-uniform-mgf
Usage
`javascript`
var mgf = require( '@stdlib/stats-base-dists-discrete-uniform-mgf' );
#### mgf( t, a, b )
Evaluates the [moment-generating function][mgf] (MGF) for a [discrete uniform][discrete-uniform-distribution] distribution with parameters a (minimum support) and b (maximum support).
`javascript
var y = mgf( 2.0, 0, 4 );
// returns ~689.475
y = mgf( -0.2, 0, 4 );
// returns ~0.697
y = mgf( 2.0, 0, 1 );
// returns ~4.195
`
If a or b is not an integer value, the function returns NaN.
`javascript`
var y = mgf( 0.2, 1, 5.5 );
// returns NaN
If provided a > b, the function returns NaN.
`javascript`
var y = mgf( 0.5, 3, 2);
// returns NaN
If provided NaN for any parameter, the function returns NaN.
`javascript
var y = mgf( NaN, 0, 1 );
// returns NaN
y = mgf( 0.0, NaN, 1 );
// returns NaN
y = mgf( 0.0, 0, NaN );
// returns NaN
`
#### mgf.factory( a, b )
Returns a function for evaluating the [moment-generating function][mgf] (MGF) of a [discrete uniform][discrete-uniform-distribution] distribution with parameters a (minimum support) and b (maximum support).
`javascript
var mymgf = mgf.factory( 6, 7 );
var y = mymgf( 0.1 );
// returns ~1.918
y = mymgf( 1.1 );
// returns ~1471.722
`
Examples
`javascript
var randint = require( '@stdlib/random-base-discrete-uniform' );
var randu = require( '@stdlib/random-base-randu' );
var mgf = require( '@stdlib/stats-base-dists-discrete-uniform-mgf' );
var randa = randint.factory( 0, 5 );
var randb = randint.factory();
var a;
var b;
var t;
var v;
var i;
for ( i = 0; i < 10; i++ ) {
t = randu();
a = randa();
b = randb( a, a+randa() );
v = mgf( t, a, b );
console.log( 't: %d, a: %d, b: %d, M_X(t;a,b): %d', t.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), v.toFixed( 4 ) );
}
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/discrete-uniform/mgf.h"
#### stdlib_base_dists_discrete_uniform_mgf( t, a, b )
Evaluates the [moment-generating function][mgf] (MGF) for a [discrete uniform][discrete-uniform-distribution] distribution with parameters a (minimum support) and b (maximum support).
`c`
double out = stdlib_base_dists_discrete_uniform_mgf( 2.0, 0, 4 );
// returns ~689.475
The function accepts the following arguments:
- t: [in] double input value.[in] int32_t
- a: minimum support.[in] int32_t
- b: maximum support.
`c`
double stdlib_base_dists_discrete_uniform_mgf( const double t, const int32_t a, const int32_t b );
$3
`c
#include "stdlib/stats/base/dists/discrete-uniform/mgf.h"
#include "stdlib/math/base/special/round.h"
#include
#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 ) {
int32_t a;
int32_t b;
double t;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
t = random_uniform( -10.0, 10.0 );
a = stdlib_base_round( random_uniform( 0.0, 10.0 ) );
b = stdlib_base_round( random_uniform( 0.0, 10.0 ) ) + a;
y = stdlib_base_dists_discrete_uniform_mgf( t, a, b );
printf( "t: %lf, a: %d, b: %d, M_X(t;a,b): %lf\n", t, a, b, 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
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[discrete-uniform-distribution]: https://en.wikipedia.org/wiki/Discrete_uniform_distribution
[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function