Logarithm of Probability Density Function

Fréchet distribution logarithm of probability density function.

The probability density function for a Fréchet random variable is

where α > 0 is the shape, s > 0 the scale and m the location parameter.

Installation

npm install @stdlib/stats-base-dists-frechet-logpdf

Usage

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

logpdf( x, alpha, s, m )

Evaluates the logarithm of the probability density function (PDF) for a Fréchet distribution with shape alpha, scale s, and location m at a value x.

var y = logpdf( 10.0, 2.0, 3.0, 5.0 );
// returns ~-2.298

y = logpdf( -3.0, 1.0, 2.0, -4.0 );
// returns ~-1.307

y = logpdf( 0.0, 2.0, 1.0, -1.0 );
// returns ~-0.307

If provided x <= m, the function returns -Infinity.

y = logpdf( -2.0, 2.0, 1.0, -1.0 );
// returns -Infinity

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

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

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

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

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

If provided alpha <= 0, the function returns NaN.

var y = logpdf( 2.0, -0.1, 1.0, 1.0 );
// returns NaN

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

If provided s <= 0, the function returns NaN.

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

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

logpdf.factory( alpha, s, m )

Returns a function for evaluating the logarithm of the probability density function of a Fréchet distribution with shape alpha, scale s, and location m.

var mylogpdf = logpdf.factory( 3.0, 3.0, 5.0 );

var y = mylogpdf( 10.0 );
// returns ~-2.259

y = mylogpdf( 7.0 );
// returns ~-1.753

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-frechet-logpdf' );

var alpha;
var m;
var s;
var x;
var y;
var i;

for ( i = 0; i < 100; i++ ) {
    alpha = randu() * 10.0;
    x = randu() * 10.0;
    s = randu() * 10.0;
    m = randu() * 10.0;
    y = logpdf( x, alpha, s, m );
    console.log( 'x: %d, α: %d, s: %d, m: %d, ln(f(x;α,s,m)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), s.toFixed( 4 ), m.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.

Copyright

Copyright © 2016-2024. The Stdlib Authors.