Probability Density Function

Logistic distribution probability density function (PDF).

The probability density function (PDF) for a logistic random variable is

f left-parenthesis x semicolon mu comma s right-parenthesis equals StartFraction e Superscript minus StartFraction x minus mu Over s EndFraction Baseline Over s left-parenthesis 1 plus e Superscript minus StartFraction x minus mu Over s EndFraction Baseline right-parenthesis squared EndFraction

where mu is the location parameter and s is the scale parameter.

Usage

var pdf = require( '@stdlib/math/base/dists/logistic/pdf' );

pdf( x, mu, s )

Evaluates the probability density function (PDF) for a logistic distribution with parameters mu (location parameter) and s (scale parameter).

var y = pdf( 2.0, 0.0, 1.0 );
// returns ~0.105

y = pdf( -1.0, 4.0, 4.0 );
// returns ~0.043

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

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

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

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

If provided s < 0, the function returns NaN.

var y = pdf( 2.0, 0.0, -1.0 );
// returns NaN

If provided s = 0, the function evaluates the PDF of a degenerate distribution centered at mu.

var y = pdf( 2.0, 8.0, 0.0 );
// returns 0.0

y = pdf( 8.0, 8.0, 0.0 );
// returns Infinity

pdf.factory( mu, s )

Returns a function for evaluating the probability density function (PDF) of a logistic distribution with parameters mu (location parameter) and s (scale parameter).

var mypdf = pdf.factory( 10.0, 2.0 );

var y = mypdf( 10.0 );
// returns 0.125

y = mypdf( 5.0 );
// returns ~0.035

Examples

var randu = require( '@stdlib/random/base/randu' );
var pdf = require( '@stdlib/math/base/dists/logistic/pdf' );

var mu;
var s;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
    x = randu() * 10.0;
    mu = randu() * 10.0;
    s = randu() * 10.0;
    y = pdf( x, mu, s );
    console.log( 'x: %d, µ: %d, s: %d, f(x;µ,s): %d', x, mu, s, y );
}