@stdlib/stats-base-dists-cauchy-logpdf
v0.2.3TypeScript
Cauchy distribution logarithm of probability density function (logPDF).
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About stdlib...
Logarithm of Probability Density Function
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> [Cauchy][cauchy-distribution] distribution logarithm of probability density function (logPDF).
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-logpdf
Usage
`javascript`
var logpdf = require( '@stdlib/stats-base-dists-cauchy-logpdf' );
#### logpdf( x, x0, gamma )
Evaluates the natural logarithm of 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 = 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 ~-2.349
`
If provided NaN as any argument, the function returns NaN.
`javascript
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 NaN
`
If provided gamma <= 0, the function returns NaN.
`javascript`
var y = logpdf( 2.0, 0.0, -1.0 );
// returns NaN
#### logpdf.factory( x0, gamma )
Returns a function for evaluating the natural logarithm of the [PDF][pdf] of a [Cauchy][cauchy-distribution] distribution with location parameter x0 and scale parameter gamma.
`javascript
var mylogpdf = logpdf.factory( 10.0, 2.0 );
var y = mylogpdf( 10.0 );
// returns ~-1.838
y = mylogpdf( 5.0 );
// returns ~-3.819
`
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
`javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var logpdf = require( '@stdlib/stats-base-dists-cauchy-logpdf' );
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, ln(f(x;x0,γ)): %0.4f', x, x0, gamma, logpdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/cauchy/logpdf.h"
#### stdlib_base_dists_cauchy_logpdf( x, x0, gamma )
Evaluates the natural logarithm of 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_logpdf( 2.0, 1.0, 1.0 );
// returns ~-1.838
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_logpdf( const double x, const double x0, const double gamma );
$3
`c
#include "stdlib/stats/base/dists/cauchy/logpdf.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_logpdf( x, x0, gamma );
printf( "x: %lf, x0: %lf, γ: %lf, ln(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