@stdlib/stats-base-dists-exponential-mgf
v0.3.1TypeScript
Exponential distribution moment-generating function (MGF).
0/weekUpdated 3 days agoApache-2.0Unpacked: 53.0 KB
Published by The Stdlib Authors
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About stdlib...
Moment-Generating Function
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
> [Exponential][exponential-distribution] distribution moment-generating function (MGF).
The [moment-generating function][mgf] for an [exponential][exponential-distribution] random variable is
where lambda > 0 is the rate parameter. For t >= lambda, the [MGF][mgf] is undefined.
Installation
``bash`
npm install @stdlib/stats-base-dists-exponential-mgf
Usage
`javascript`
var mgf = require( '@stdlib/stats-base-dists-exponential-mgf' );
#### mgf( t, lambda )
Evaluates the moment-generating function ([MGF][mgf]) for an [exponential][exponential-distribution] distribution.
`javascript
var y = mgf( 2.0, 3.0 );
// returns 3.0
y = mgf( 0.4, 1.2 );
// returns 1.5
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = mgf( NaN, 0.0 );
// returns NaN
y = mgf( 0.0, NaN );
// returns NaN
`
If provided lambda < 0 or t >= lambda, the function returns NaN.
`javascript
var y = mgf( -2.0, -1.0 );
// returns NaN
y = mgf( 3.0, 2.0 );
// returns NaN
`
#### mgf.factory( lambda )
Returns a function for evaluating the [moment-generating function][mgf] of an [exponential][exponential-distribution] distribution with parameter lambda(rate parameter).
`javascript`
var mymgf = mgf.factory( 4.0 );
var y = mymgf( 3.0 );
// returns 4.0
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var mgf = require( '@stdlib/stats-base-dists-exponential-mgf' );
var opts = {
'dtype': 'float64'
};
var t = uniform( 10, 0.0, 10.0, opts );
var lambda = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, λ: %0.4f, M_X(t;λ): %0.4f', t, lambda, mgf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/exponential/mgf.h"
#### stdlib_base_dists_exponential_mgf( t, lambda )
Evaluates the moment-generating function ([MGF][mgf]) for an [exponential][exponential-distribution] distribution.
`c`
double out = stdlib_base_dists_exponential_mgf( 2.0, 3.0 );
// returns 3.0
The function accepts the following arguments:
- t: [in] double input value.[in] double
- lambda: rate parameter.
`c`
double stdlib_base_dists_exponential_mgf( const double t, const double lambda );
$3
`c
#include "stdlib/stats/base/dists/exponential/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 lambda;
double t;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
t = random_uniform( -1.0, 1.0 );
lambda = random_uniform( 1.1, 10.0 );
y = stdlib_base_dists_exponential_mgf( t, lambda );
printf( "t: %lf, λ: %lf, M_X(t;λ): %lf\n", t, lambda, 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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[umd]: https://github.com/umdjs/umd
[es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules
[deno-url]: https://github.com/stdlib-js/stats-base-dists-exponential-mgf/tree/deno
[deno-readme]: https://github.com/stdlib-js/stats-base-dists-exponential-mgf/blob/deno/README.md
[umd-url]: https://github.com/stdlib-js/stats-base-dists-exponential-mgf/tree/umd
[umd-readme]: https://github.com/stdlib-js/stats-base-dists-exponential-mgf/blob/umd/README.md
[esm-url]: https://github.com/stdlib-js/stats-base-dists-exponential-mgf/tree/esm
[esm-readme]: https://github.com/stdlib-js/stats-base-dists-exponential-mgf/blob/esm/README.md
[branches-url]: https://github.com/stdlib-js/stats-base-dists-exponential-mgf/blob/main/branches.md
[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/stats-base-dists-exponential-mgf/main/LICENSE
[exponential-distribution]: https://en.wikipedia.org/wiki/Exponential_distribution
[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function