Logarithm of Probability Density Function

Logistic distribution logarithm of 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 logpdf = require( '@stdlib/math/base/dists/logistic/logpdf' );

logpdf( x, mu, s )

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

var y = logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.254

y = logpdf( -1.0, 4.0, 4.0 );
// returns ~-3.147

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

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

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

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

If provided s < 0, the function returns NaN.

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

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

var y = logpdf( 2.0, 8.0, 0.0 );
// returns -Infinity

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

logpdf.factory( mu, s )

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

var mylogpdf = logpdf.factory( 10.0, 2.0 );

var y = mylogpdf( 10.0 );
// returns ~-2.079

y = mylogpdf( 5.0 );
// returns ~-3.352

Examples

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

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 = logpdf( x, mu, s );
    console.log( 'x: %d, µ: %d, s: %d, ln(f(x;µ,s)): %d', x, mu, s, y );
}