Logarithm of Probability Density Function

Lévy distribution logarithm of probability density function (PDF).

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

where μ is the location parameter and c > 0 is the scale parameter.

Usage

var logpdf = require( '@stdlib/stats/base/dists/levy/logpdf' );

logpdf( x, mu, c )

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

var y = logpdf( 2.0, 0.0, 1.0 );
// returns ~-2.209

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

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 c <= 0, the function returns NaN.

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

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

logpdf.factory( mu, c )

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

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

var y = mylogpdf( 11.0 );
// returns ~-1.572

y = mylogpdf( 20.0 );
// returns ~-4.126

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 EPS = require( '@stdlib/constants/float64/eps' );
var logpdf = require( '@stdlib/stats/base/dists/levy/logpdf' );

var mu;
var c;
var x;
var y;
var i;

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