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README.md |
Moment-Generating Function
Weibull distribution moment-generating function (MGF).
The moment-generating function for a Weibull random variable is
where lambda > 0
is the scale paramater and k > 0
is the shape parameter.
Usage
var mgf = require( '@stdlib/stats/base/dists/weibull/mgf' );
mgf( t, k, lambda )
Evaluates the moment-generating function (MGF) for a Weibull distribution with shape parameter k
and scale parameter lambda
.
var y = mgf( 1.0, 1.0, 0.5);
// returns ~2.0
y = mgf( -1.0, 4.0, 4.0 );
// returns ~0.019
If provided NaN
as any argument, the function returns NaN
.
var y = mgf( NaN, 1.0, 1.0 );
// returns NaN
y = mgf( 0.0, NaN, 1.0 );
// returns NaN
y = mgf( 0.0, 1.0, NaN );
// returns NaN
If provided k <= 0
, the function returns NaN
.
var y = mgf( 0.2, -1.0, 0.5 );
// returns NaN
y = mgf( 0.2, 0.0, 0.5 );
// returns NaN
If provided lambda <= 0
, the function returns NaN
.
var y = mgf( 0.2, 0.5, -1.0 );
// returns NaN
y = mgf( 0.2, 0.5, 0.0 );
// returns NaN
mgf.factory( k, lambda )
Returns a function for evaluating the moment-generating function of a Weibull distribution with shape parameter k
and scale parameter lambda
.
var myMGF = mgf.factory( 8.0, 10.0 );
var y = myMGF( 0.8 );
// returns ~3150.149
y = myMGF( 0.08 );
// returns ~2.137
Examples
var randu = require( '@stdlib/random/base/randu' );
var EPS = require( '@stdlib/constants/float64/eps' );
var mgf = require( '@stdlib/stats/base/dists/weibull/mgf' );
var lambda;
var k;
var t;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
t = randu() * 5.0;
lambda = ( randu() * 10.0 ) + EPS;
k = ( randu() * 10.0 ) + EPS;
y = mgf( t, lambda, k );
console.log( 'x: %d, k: %d, λ: %d, M_X(t;k,λ): %d', t.toFixed( 4 ), k.toFixed( 4 ), lambda.toFixed( 4 ), y.toFixed( 4 ) );
}