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.

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 ) );
}

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 );
    }
}