time-to-botec/squiggle/node_modules/@stdlib/stats/base/dists/logistic/logpdf

Logarithm of Probability Density Function

Logistic distribution logarithm of probability density function (PDF).

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

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

Usage

var logpdf = require( '@stdlib/stats/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 ~-3.14

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 ~-3.351

Notes

• In virtually all cases, using the logpdf or logcdf functions is preferable to manually computing the logarithm of the pdf or cdf, respectively, since the latter is prone to overflow and underflow.

Examples

var randu = require( '@stdlib/random/base/randu' );
var logpdf = require( '@stdlib/stats/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 );
}