Beta distribution logarithm of probability density function (PDF).
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[Beta][beta-distribution] distribution logarithm of probability density function (PDF).
math
f(x;\alpha,\beta)= \begin{cases} \frac{\Gamma(\alpha + \beta)}{\Gamma(\alpha) + \Gamma(\beta)}{x^{\alpha-1}(1-x)^{\beta-1}} & \text{ for } x \in (0,1) \\ 0 & \text{ otherwise } \end{cases}alpha > 0 is the first shape parameter and beta > 0 is the second shape parameter.bash
npm install @stdlib/stats-base-dists-beta-logpdfscript 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 logpdf = require( '@stdlib/stats-base-dists-beta-logpdf' );alpha (first shape parameter) and beta (second shape parameter).javascript
var y = logpdf( 0.5, 0.5, 1.0 );
// returns ~-0.347
y = logpdf( 0.1, 1.0, 1.0 );
// returns 0.0
y = logpdf( 0.8, 4.0, 2.0 );
// returns ~0.717x outside the support [0,1], the function returns -Infinity.javascript
var y = logpdf( -0.1, 1.0, 1.0 );
// returns -Infinity
y = logpdf( 1.1, 1.0, 1.0 );
// returns -InfinityNaN as any argument, the function returns NaN.javascript
var y = logpdf( NaN, 1.0, 1.0 );
// returns NaN
y = logpdf( 0.0, NaN, 1.0 );
// returns NaN
y = logpdf( 0.0, 1.0, NaN );
// returns NaNalpha <= 0, the function returns NaN.javascript
var y = logpdf( 0.5, 0.0, 1.0 );
// returns NaN
y = logpdf( 0.5, -1.0, 1.0 );
// returns NaNbeta <= 0, the function returns NaN.javascript
var y = logpdf( 0.5, 1.0, 0.0 );
// returns NaN
y = logpdf( 0.5, 1.0, -1.0 );
// returns NaNfunction for evaluating the natural logarithm of the [PDF][pdf] for a [beta][beta-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).javascript
var mylogPDF = logpdf.factory( 0.5, 0.5 );
var y = mylogPDF( 0.8 );
// returns ~-0.228
y = mylogPDF( 0.3 );
// returns ~-0.364logpdf 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 logpdf = require( '@stdlib/stats-base-dists-beta-logpdf' );
var alpha;
var beta;
var x;
var y;
var i;
for ( i = 0; i < 10; i++ ) {
x = randu();
alpha = ( randu()*5.0 ) + EPS;
beta = ( randu()*5.0 ) + EPS;
y = logpdf( x, alpha, beta );
console.log( 'x: %d, α: %d, β: %d, ln(f(x;α,β)): %d', x.toFixed( 4 ), alpha.toFixed( 4 ), beta.toFixed( 4 ), y.toFixed( 4 ) );
}c
#include "stdlib/stats/base/dists/beta/logpdf.h"alpha and second shape parameter beta.c
double y = stdlib_base_dists_beta_logpdf( 0.5, 1.0, 1.0 );
// returns 0.0[in] double input value.[in] double first shape parameter.[in] double second shape parameter.c
double stdlib_base_dists_beta_logpdf( const double x, double alpha, const double beta );c
#include "stdlib/stats/base/dists/beta/logpdf.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 alpha;
double beta;
double x;
double y;
int i;
for ( i = 0; i < 10; i++ ) {
x = random_uniform( 0.0, 1.0 );
alpha = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
beta = random_uniform( STDLIB_CONSTANT_FLOAT64_EPS, 5.0 );
y = stdlib_base_dists_beta_logpdf( x, alpha, beta );
printf( "x: %lf, α: %lf, β: %lf, ln(f(x;α,β)): %lf\n", x, alpha, beta, y );
}
}
