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README.md |
Moment-Generating Function
Binomial distribution moment-generating function (MGF).
The moment-generating function for a binomial random variable is
where the nonnegative integer n
is the number of trials and 0 <= p <= 1
is the success probability.
Usage
var mgf = require( '@stdlib/stats/base/dists/binomial/mgf' );
mgf( t, n, p )
Evaluates the moment-generating function for a binomial distribution with number of trials n
and success probability p
.
var y = mgf( 0.5, 20, 0.2 );
// returns ~11.471
y = mgf( 5.0, 20, 0.2 );
// returns ~4.798e29
y = mgf( 0.9, 10, 0.4 );
// returns ~99.338
y = mgf( 0.0, 10, 0.4 );
// returns 1.0
If provided NaN
as any argument, the function returns NaN
.
var y = mgf( NaN, 20, 0.5 );
// returns NaN
y = mgf( 0.0, NaN, 0.5 );
// returns NaN
y = mgf( 0.0, 20, NaN );
// returns NaN
If provided a number of trials n
which is not a nonnegative integer, the function returns NaN
.
var y = mgf( 0.2, 1.5, 0.5 );
// returns NaN
y = mgf( 0.2, -2.0, 0.5 );
// returns NaN
If provided a success probability p
outside of [0,1]
, the function returns NaN
.
var y = mgf( 0.2, 20, -1.0 );
// returns NaN
y = mgf( 0.2, 20, 1.5 );
// returns NaN
mgf.factory( n, p )
Returns a function for evaluating the moment-generating function of a binomial distribution with number of trials n
and success probability p
.
var myMGF = mgf.factory( 10, 0.5 );
var y = myMGF( 0.3 );
// returns ~5.013
Examples
var randu = require( '@stdlib/random/base/randu' );
var round = require( '@stdlib/math/base/special/round' );
var mgf = require( '@stdlib/stats/base/dists/binomial/mgf' );
var n;
var p;
var t;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
t = round( randu() * 5.0 );
n = round( randu() * 10.0 );
p = randu();
y = mgf( t, n, p );
console.log( 't: %d, n: %d, p: %d, M_X(t;n,p): %d', t, n, p.toFixed( 4 ), y.toFixed( 4 ) );
}