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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.
npm install @stdlib/stats-base-dists-frechet-logpdfAlternatively,
- To load the package in a website via a
scripttag without installation and bundlers, use the ES Module available on theesmbranch (see README). - If you are using Deno, visit the
denobranch (see README for usage intructions). - For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the
umdbranch (see README).
The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.
To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.
var logpdf = require( '@stdlib/stats-base-dists-frechet-logpdf' );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 ~-0.307If provided x <= m, the function returns -Infinity.
y = logpdf( -2.0, 2.0, 1.0, -1.0 );
// returns -InfinityIf 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 NaNIf 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 NaNIf 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 NaNReturns 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- In virtually all cases, using the
logpdforlogcdffunctions is preferable to manually computing the logarithm of thepdforcdf, respectively, since the latter is prone to overflow and underflow.
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 ) );
}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.
See LICENSE.
Copyright © 2016-2024. The Stdlib Authors.
