@stdlib/stats-base-dists-cauchy-pdf
v0.2.3TypeScript
Cauchy distribution probability density function (PDF).
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Published by The Stdlib Authors
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Probability Density Function
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> [Cauchy][cauchy-distribution] distribution probability density function (PDF).
The [probability density function][pdf] (PDF) for a [Cauchy][cauchy-distribution] random variable is
where x0 is the location parameter and gamma > 0 is the scale parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-cauchy-pdf
Usage
`javascript`
var pdf = require( '@stdlib/stats-base-dists-cauchy-pdf' );
#### pdf( x, x0, gamma )
Evaluates the [probability density function][pdf] (PDF) for a [Cauchy][cauchy-distribution] distribution with parameters x0 (location parameter) and gamma > 0 (scale parameter).
`javascript
var y = pdf( 2.0, 1.0, 1.0 );
// returns ~0.159
y = pdf( 4.0, 3.0, 0.1 );
// returns ~0.0315
y = pdf( 4.0, 3.0, 3.0 );
// returns ~0.095
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pdf( NaN, 1.0, 1.0 );
// returns NaN
y = pdf( 2.0, NaN, 1.0 );
// returns NaN
y = pdf( 2.0, 1.0, NaN );
// returns NaN
`
If provided gamma <= 0, the function returns NaN.
`javascript
var y = pdf( 2.0, 0.0, -1.0 );
// returns NaN
y = pdf( 2.0, 0.0, 0.0 );
// returns NaN
`
#### pdf.factory( x0, gamma )
Returns a function for evaluating the [PDF][pdf] of a [Cauchy][cauchy-distribution] distribution with location parameter x0 and scale parameter gamma.
`javascript
var mypdf = pdf.factory( 10.0, 2.0 );
var y = mypdf( 10.0 );
// returns ~0.159
y = mypdf( 5.0 );
// returns ~0.022
`
Examples
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var pdf = require( '@stdlib/stats-base-dists-cauchy-pdf' );
var opts = {
'dtype': 'float64'
};
var gamma = uniform( 10, EPS, 20.0, opts );
var x0 = uniform( 10, -5.0, 5.0, opts );
var x = uniform( 10, 0.0, 10.0, opts );
logEachMap( 'x: %0.4f, x0: %0.4f, γ: %0.4f, f(x;x0,γ): %0.4f', x, x0, gamma, pdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/cauchy/pdf.h"
#### stdlib_base_dists_cauchy_pdf( x, x0, gamma )
Evaluates the [probability density function][pdf] (PDF) for a [Cauchy][cauchy-distribution] distribution with parameters x0 (location parameter) and gamma > 0 (scale parameter).
`c`
double out = stdlib_base_dists_cauchy_pdf( 0.5, 0.0, 2.0 );
// returns ~0.333
The function accepts the following arguments:
- x: [in] double input value.[in] double
- x0: location parameter.[in] double
- gamma: scale parameter.
`c`
double stdlib_base_dists_cauchy_pdf( const double x, const double x0, const double gamma );
$3
`c
#include "stdlib/stats/base/dists/cauchy/pdf.h"
#include "stdlib/constants/float64/eps.h"
#include
#include
static double random_uniform( const double min, const double max ) {
double v = (double)rand() / ( (double)RAND_MAX + 1.0 );
return min + ( v*(max-min) );
}
int main( void ) {
double gamma;
double x0;
double x;
double y;
int i;
for ( i = 0; i < 25; i++ ) {
x = random_uniform( 0.0, 10.0 );
x0 = random_uniform( -5.0, 5.0 );
gamma = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 20.0 );
y = stdlib_base_dists_cauchy_pdf( x, x0, gamma );
printf( "x: %lf, k: %lf, γ: %lf, f(x;x0,γ): %lf\n", x, x0, gamma, y );
}
}
`
*
Notice
This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].
#### Community
[![Chat][chat-image]][chat-url]
---
License
See [LICENSE][stdlib-license].
Copyright
Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[pdf]: https://en.wikipedia.org/wiki/Probability_density_function
[cauchy-distribution]: https://en.wikipedia.org/wiki/Cauchy_distribution