README.md

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Moment-Generating Function

Triangular distribution moment-generating function (MGF).

The moment-generating function for a triangular random variable is

$$M_X(t) := \mathbb{E}\!\left[e^{tX}\right] = 2\frac{(b\!-\!c)e^{at}\!-\!(b\!-\!a)e^{ct}\!+\!(c\!-\!a)e^{bt}} {(b-a)(c-a)(b-c)t^2}$$

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.

Usage

import mgf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-triangular-mgf@deno/mod.js';

You can also import the following named exports from the package:

import { factory } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-triangular-mgf@deno/mod.js';

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

import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@deno/mod.js';
import mgf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-triangular-mgf@deno/mod.js';

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 ) );
}

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C APIs

Usage

#include "stdlib/stats/base/dists/triangular/mgf.h"

stdlib_base_dists_triangular_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).

double y = stdlib_base_dists_triangular_mgf( 0.5, -1.0, 1.0, 0.0 );
// returns ~1.021

The function accepts the following arguments:

• t: [in] double input value.
• a: [in] double lower limit.
• b: [in] double upper limit.
• c: [in] double mode.

double stdlib_base_dists_triangular_mgf( const double t, const double a, const double b, const double c );

Examples

#include "stdlib/stats/base/dists/triangular/mgf.h"
#include "stdlib/constants/float64/eps.h"
#include <stdlib.h>
#include <stdio.h>

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 a;
    double b;
    double c;
    double t;
    double y;
    int i;

    for ( i = 0; i < 25; i++ ) {
        t = random_uniform( 0.0, 5.0 );
        a = random_uniform( 0.0, 10.0 );
        b = random_uniform( a+STDLIB_CONSTANT_FLOAT64_EPS, 40.0 );
        c = random_uniform( a, b );
        y = stdlib_base_dists_triangular_mgf( t, a, b, c );
        printf( "t: %lf, a: %lf, b: %lf, c: %lf, M_X(t;a,b,c): %lf\n", t, a, b, c, y );
    }
}

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Notice

This package is part of stdlib, a standard library 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

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License

See LICENSE.

Copyright

Copyright © 2016-2025. The Stdlib Authors.