Cauchy distribution natural logarithm of cumulative distribution function (CDF).
We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we’ve built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.
The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.
When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.
To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!
[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]
[Cauchy][cauchy-distribution] distribution logarithm of [cumulative distribution function][cdf].
math
F(x; x_0,\gamma)=\frac{1}{\pi} \mathop{\mathrm{arctan}} \left(\frac{x-x_0}{\gamma}\right)+\frac{1}{2}x0 is the location parameter and gamma > 0 is the scale parameter.bash
npm install @stdlib/stats-base-dists-cauchy-logcdfscript tag without installation and bundlers, use the [ES Module][es-module] available on the [esm][esm-url] branch (see [README][esm-readme]).deno][deno-url] branch (see [README][deno-readme] for usage intructions).umd][umd-url] branch (see [README][umd-readme]).javascript
var logcdf = require( '@stdlib/stats-base-dists-cauchy-logcdf' );x0 (location parameter) and gamma > 0 (scale parameter).javascript
var y = logcdf( 4.0, 0.0, 2.0 );
// returns ~-0.16
y = logcdf( 1.0, 0.0, 2.0 );
// returns ~-0.435
y = logcdf( 1.0, 3.0, 2.0 );
// returns ~-1.386NaN as any argument, the function returns NaN.javascript
var y = logcdf( NaN, 0.0, 2.0 );
// returns NaN
y = logcdf( 1.0, 2.0, NaN );
// returns NaN
y = logcdf( 1.0, NaN, 3.0 );
// returns NaNgamma <= 0, the function returns NaN.javascript
var y = logcdf( 2.0, 0.0, -1.0 );
// returns NaN
y = logcdf( 2.0, 0.0, 0.0 );
// returns NaNx0 (location parameter) and gamma > 0 (scale parameter).javascript
var mylogcdf = logcdf.factory( 10.0, 2.0 );
var y = mylogcdf( 10.0 );
// returns ~-0.693
y = mylogcdf( 12.0 );
// returns ~-0.288logpdf 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.javascript
var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var logcdf = require( '@stdlib/stats-base-dists-cauchy-logcdf' );
var gamma;
var x0;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu() * 10.0;
x0 = randu() * 10.0;
gamma = ( randu()*10.0 ) + EPS;
y = logcdf( x, x0, gamma );
console.log( 'x: %d, x0: %d, γ: %d, ln(F(x;x0,γ)): %d', x, x0, gamma, y );
}c
#include "stdlib/stats/base/dists/cauchy/logcdf.h"x0 (location parameter) and gamma > 0 (scale parameter).c
double out = stdlib_base_dists_cauchy_logcdf( 4.0, 0.0, 2.0 );
// returns ~-0.16[in] double input value.[in] double location parameter.[in] double scale parameter.c
double stdlib_base_dists_cauchy_logcdf( const double x, const double x0, const double gamma );c
#include "stdlib/stats/base/dists/cauchy/logcdf.h"
#include "stdlib/constants/float64/eps.h"
#include <stdlib.h>
#include <stdio.h>
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( 0.0, 10.0 );
gamma = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 10.0 );
y = stdlib_base_dists_cauchy_logcdf( x, x0, gamma );
printf( "x: %lf, x0: %lf, γ: %lf, ln(F(x;x0,γ)): %lf\n", x, x0, gamma, y );
}
}
