@stdlib/stats-base-dists-exponential-mgf
v0.2.2
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Exponential distribution moment-generating function (MGF).
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Moment-Generating Function
Exponential distribution moment-generating function (MGF).
The moment-generating function for an exponential random variable is
where lambda > 0
is the rate parameter. For t >= lambda
, the MGF is undefined.
Installation
npm install @stdlib/stats-base-dists-exponential-mgf
Usage
var mgf = require( '@stdlib/stats-base-dists-exponential-mgf' );
mgf( t, lambda )
Evaluates the moment-generating function (MGF) for an exponential distribution.
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
.
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
.
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 of an exponential distribution with parameter lambda
(rate parameter).
var mymgf = mgf.factory( 4.0 );
var y = mymgf( 3.0 );
// returns 4.0
Examples
var randu = require( '@stdlib/random-base-randu' );
var mgf = require( '@stdlib/stats-base-dists-exponential-mgf' );
var lambda;
var t;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
t = randu() * 10.0;
lambda = randu() * 10.0;
y = mgf( t, lambda );
console.log( 'x: %d, λ: %d, M_X(t;λ): %d', t.toFixed( 4 ), lambda.toFixed( 4 ), y.toFixed( 4 ) );
}
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 © 2016-2024. The Stdlib Authors.