README

Moment-Generating Function

Logistic distribution moment-generating function (MGF).

The moment-generating function for a logistic random variable is

Moment-generating function (MGF) for a logistic distribution.

for st ∈ (-1,1), where mu is the location parameter and s is the scale parameter. In above equation, B denotes the Beta function. For st outside the interval (-1,1), the function is not defined.

Installation

npm install @stdlib/stats-base-dists-logistic-mgf

Usage

var mgf = require( '@stdlib/stats-base-dists-logistic-mgf' );

mgf( t, mu, s )

Evaluates the logarithm of the moment-generating function (MGF) for a logistic distribution with parameters mu (location parameter) and s (scale parameter).

var y = mgf( 0.9, 0.0, 1.0 );
// returns ~9.15

y = mgf( 0.1, 4.0, 4.0 );
// returns ~1.971

y = mgf( -0.2, 4.0, 4.0 );
// returns ~1.921

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

var y = mgf( NaN, 0.0, 1.0 );
// returns NaN

y = mgf( 0.0, NaN, 1.0 );
// returns NaN

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

If provided s < 0 or abs( s * t ) > 1, the function returns NaN.

var y = mgf( 0.5, 0.0, -1.0 );
// returns NaN

y = mgf( 0.5, 0.0, 4.0 );
// returns NaN

mgf.factory( mu, s )

Returns a function for evaluating the moment-generating function (MGF) of a logistic distribution with parameters mu (location parameter) and s (scale parameter).

var mymgf = mgf.factory( 10.0, 0.5 );

var y = mymgf( 0.5 );
// returns ~164.846

y = mymgf( 2.0 );
// returns Infinity

Examples

var randu = require( '@stdlib/random-base-randu' );
var mgf = require( '@stdlib/stats-base-dists-logistic-mgf' );

var mu;
var s;
var t;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    t = randu();
    mu = (randu() * 10.0) - 5.0;
    s = randu() * 2.0;
    y = mgf( t, mu, s );
    console.log( 't: %d, µ: %d, s: %d, M_X(t;µ,s): %d', t.toFixed( 4 ), mu.toFixed( 4 ), s.toFixed( 4 ), y.toFixed( 4 ) );
}

Notice

This package is part of 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, see the main project repository.

Community

License

See LICENSE.

@stdlib/stats-base-dists-logistic-mgf

Usage no npm install needed!