# Moment-Generating Function

Exponential distribution moment-generating function (MGF).

The moment-generating function for an exponential random variable is

where lambda > 0 is the rate parameter. For t >= lambda, the MGF is undefined.

## Usage

var mgf = require( '@stdlib/math/base/dists/exponential/mgf' );


#### mgf( t, lambda )

Evaluates the moment-generating function (MGF) for an exponential distribution.

var y = mgf( 2.0, 3.0 );
// returns 3.0

y = mgf( 0.4, 1.2 );
// returns 1.5


If provided NaN as any argument, the function returns NaN.

var y = mgf( NaN, 0.0 );
// returns NaN

y = mgf( 0.0, NaN );
// returns NaN


If provided lambda < 0 or t >= lambda, the function returns NaN.

var y = mgf( -2.0, -1.0 );
// returns NaN

y = mgf( 3.0, 2.0 );
// returns NaN


#### mgf.factory( lambda )

Returns a function for evaluating the moment-generating function of an exponential distribution with parameter lambda(rate parameter).

var mymgf = mgf.factory( 4.0 );
var y = mymgf( 3.0 );
// returns 4.0


## Examples

var randu = require( '@stdlib/random/base/randu' );
var mgf = require( '@stdlib/math/base/dists/exponential/mgf' );

var lambda;
var t;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
t = randu() * 10.0;
lambda = randu() * 10.0;
y = mgf( t, lambda );
console.log( 'x: %d, λ: %d, M_X(t;λ): %d', t.toFixed( 4 ), lambda.toFixed( 4 ), y.toFixed( 4 ) );
}