@stdlib/stats-base-dists-triangular-mgf
v0.3.1TypeScript
Triangular distribution moment-generating function (MGF).
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Published by The Stdlib Authors
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About stdlib...
Moment-Generating Function
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> [Triangular][triangular-distribution] distribution moment-generating function (MGF).
The [moment-generating function][mgf] for a [triangular][triangular-distribution] 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
``bash`
npm install @stdlib/stats-base-dists-triangular-mgf
Usage
`javascript`
var mgf = require( '@stdlib/stats-base-dists-triangular-mgf' );
#### mgf( t, a, b, c )
Evaluates the [moment-generating function][mgf] (MGF) for a [triangular][triangular-distribution] distribution with parameters a (lower limit), b (upper limit), and c (mode).
`javascript
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.
`javascript
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.
`javascript
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][mgf] of a [triangular][triangular-distribution] distribution with parameters a (lower limit), b (upper limit), and c (mode).
`javascript
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
`javascript
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
$3
`c`
#include "stdlib/stats/base/dists/triangular/mgf.h"
#### stdlib_base_dists_triangular_mgf( t, a, b, c )
Evaluates the [moment-generating function][mgf] (MGF) for a [triangular][triangular-distribution] distribution with parameters a (lower limit), b (upper limit), and c (mode).
`c`
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.[in] double
- a: lower limit.[in] double
- b: upper limit.[in] double
- c: mode.
`c`
double stdlib_base_dists_triangular_mgf( const double t, const double a, const double b, const double c );
$3
`c
#include "stdlib/stats/base/dists/triangular/mgf.h"
#include "stdlib/constants/float64/eps.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 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 );
}
}
`
*
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
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---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[triangular-distribution]: https://en.wikipedia.org/wiki/Triangular_distribution
[mgf]: https://en.wikipedia.org/wiki/Moment-generating_function