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README.md |
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 ) );
}