Moment-Generating Function

Triangular distribution moment-generating function (MGF).

The moment-generating function for a triangular random variable is

where a is the lower limit, b is the upper limit, and c is the mode of the distribution. The parameters must satisfy b > a and a <= b <= c.

Installation

npm install @stdlib/stats-base-dists-triangular-mgf

Usage

var mgf = require( '@stdlib/stats-base-dists-triangular-mgf' );

mgf( t, a, b, c )

Evaluates the moment-generating function (MGF) for a triangular distribution with parameters a (lower limit), b (upper limit), and c (mode).

var y = mgf( 0.5, -1.0, 1.0, 0.0 );
// returns ~1.021

y = mgf( 0.5, -1.0, 1.0, 0.5 );
// returns ~1.111

y = mgf( -0.3, -20.0, 0.0, -2.0 );
// returns ~24.334

y = mgf( -2.0, -1.0, 1.0, 0.0 );
// returns ~1.381

If provided NaN as any argument, the function returns NaN.

var y = mgf( NaN, 0.0, 1.0, 0.5 );
// returns NaN

y = mgf( 0.0, NaN, 1.0, 0.5 );
// returns NaN

y = mgf( 0.0, 0.0, NaN, 0.5 );
// returns NaN

y = mgf( 2.0, 1.0, 0.0, NaN );
// returns NaN

If provided parameters not satisfying a <= c <= b, the function returns NaN.

var y = mgf( 2.0, 1.0, 0.0, 1.5 );
// returns NaN

y = mgf( 2.0, 1.0, 0.0, -1.0 );
// returns NaN

y = mgf( 2.0, 0.0, -1.0, 0.5 );
// returns NaN

mgf.factory( a, b, c )

Returns a function for evaluating the moment-generating function of a triangular distribution with parameters a (lower limit), b (upper limit), and c (mode).

var mymgf = mgf.factory( 0.0, 2.0, 1.0 );

var y = mymgf( -1.0 );
// returns ~0.3996

y = mymgf( 2.0 );
// returns ~10.205

Examples

var randu = require( '@stdlib/random-base-randu' );
var mgf = require( '@stdlib/stats-base-dists-triangular-mgf' );

var a;
var b;
var c;
var t;
var v;
var i;

for ( i = 0; i < 10; i++ ) {
    t = randu() * 5.0;
    a = randu() * 10.0;
    b = a + (randu() * 40.0);
    c = a + (( b - a ) * randu());
    v = mgf( t, a, b, c );
    console.log( 't: %d, a: %d, b: %d, c: %d, M_X(t;a,b,c): %d', t.toFixed( 4 ), a.toFixed( 4 ), b.toFixed( 4 ), c.toFixed( 4 ), v.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.