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Cauchy distribution logarithm of probability density function (logPDF).
The probability density function (PDF) for a Cauchy random variable is
where x0 is the location parameter and gamma > 0 is the scale parameter.
import logpdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-cauchy-logpdf@esm/index.mjs';You can also import the following named exports from the package:
import { factory } from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-cauchy-logpdf@esm/index.mjs';Evaluates the natural logarithm of the probability density function (PDF) for a Cauchy distribution with parameters x0 (location parameter) and gamma > 0 (scale parameter).
var y = logpdf( 2.0, 1.0, 1.0 );
// returns ~-1.838
y = logpdf( 4.0, 3.0, 0.1 );
// returns ~-3.457
y = logpdf( 4.0, 3.0, 3.0 );
// returns ~-2.349If provided NaN as any argument, the function returns NaN.
var y = logpdf( NaN, 1.0, 1.0 );
// returns NaN
y = logpdf( 2.0, NaN, 1.0 );
// returns NaN
y = logpdf( 2.0, 1.0, NaN );
// returns NaNIf provided gamma <= 0, the function returns NaN.
var y = logpdf( 2.0, 0.0, -1.0 );
// returns NaNReturns a function for evaluating the natural logarithm of the PDF of a Cauchy distribution with location parameter x0 and scale parameter gamma.
var mylogpdf = logpdf.factory( 10.0, 2.0 );
var y = mylogpdf( 10.0 );
// returns ~-1.838
y = mylogpdf( 5.0 );
// returns ~-3.819- 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.
<!DOCTYPE html>
<html lang="en">
<body>
<script type="module">
import randu from 'https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@esm/index.mjs';
import EPS from 'https://cdn.jsdelivr.net/gh/stdlib-js/constants-float64-eps@esm/index.mjs';
import logpdf from 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-base-dists-cauchy-logpdf@esm/index.mjs';
var gamma;
var x0;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu() * 10.0;
x0 = ( randu()*10.0 ) - 5.0;
gamma = ( randu()*20.0 ) + EPS;
y = logpdf( x, gamma, x0 );
console.log( 'x: %d, x0: %d, γ: %d, ln(f(x;x0,γ)): %d', x.toFixed(4), x0.toFixed(4), gamma.toFixed(4), y.toFixed(4) );
}
</script>
</body>
</html>This package is part of stdlib, a standard library 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 © 2016-2025. The Stdlib Authors.
