@stdlib/stats-base-dists-betaprime-pdf
v0.3.1TypeScript
Beta prime 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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> [Beta prime][betaprime-distribution] distribution probability density function (PDF).
The [probability density function][pdf] (PDF) for a [beta prime][betaprime-distribution] random variable is
where α > 0 is the first shape parameter and β > 0 is the second shape parameter.
Installation
``bash`
npm install @stdlib/stats-base-dists-betaprime-pdf
Usage
`javascript`
var pdf = require( '@stdlib/stats-base-dists-betaprime-pdf' );
#### pdf( x, alpha, beta )
Evaluates the [probability density function][pdf] (PDF) for a [beta prime][betaprime-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).
`javascript
var y = pdf( 0.5, 0.5, 1.0 );
// returns ~0.385
y = pdf( 0.1, 1.0, 1.0 );
// returns ~0.826
y = pdf( 0.8, 4.0, 2.0 );
// returns ~0.301
`
If provided a x <= 0, the function returns 0.
`javascript
var y = pdf( -0.1, 1.0, 1.0 );
// returns 0.0
y = pdf( 0.0, 1.0, 1.0 );
// returns 0.0
`
If provided NaN as any argument, the function returns NaN.
`javascript
var y = pdf( NaN, 1.0, 1.0 );
// returns NaN
y = pdf( 0.0, NaN, 1.0 );
// returns NaN
y = pdf( 0.0, 1.0, NaN );
// returns NaN
`
If provided alpha <= 0, the function returns NaN.
`javascript
var y = pdf( 0.5, 0.0, 1.0 );
// returns NaN
y = pdf( 0.5, -1.0, 1.0 );
// returns NaN
`
If provided beta <= 0, the function returns NaN.
`javascript
var y = pdf( 0.5, 1.0, 0.0 );
// returns NaN
y = pdf( 0.5, 1.0, -1.0 );
// returns NaN
`
#### pdf.factory( alpha, beta )
Returns a function for evaluating the [PDF][pdf] for a [beta prime][betaprime-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).
`javascript
var mypdf = pdf.factory( 0.5, 0.5 );
var y = mypdf( 0.8 );
// returns ~0.198
y = mypdf( 0.3 );
// returns ~0.447
`
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-betaprime-pdf' );
var opts = {
'dtype': 'float64'
};
var alpha = uniform( 10, EPS, 5.0, opts );
var beta = uniform( 10, EPS, 5.0, opts );
var x = uniform( 10, 0.0, 1.0, opts );
logEachMap( 'x: %0.4f, α: %0.4f, β: %0.4f, f(x;α,β): %0.4f', x, alpha, beta, pdf );
`
*
C APIs
$3
`c`
#include "stdlib/stats/base/dists/betaprime/pdf.h"
#### stdlib_base_dists_betaprime_pdf( x, alpha, beta )
Evaluates the [probability density function][pdf] (PDF) for a [beta prime][betaprime-distribution] distribution with parameters alpha (first shape parameter) and beta (second shape parameter).
`c`
double y = stdlib_base_dists_betaprime_pdf( 0.5, 1.0, 1.0 );
// returns ~0.444
The function accepts the following arguments:
- x: [in] double input value.[in] double
- alpha: first shape parameter.[in] double
- beta: second shape parameter.
`c`
double stdlib_base_dists_betaprime_pdf( const double x, const double alpha, const double beta );
$3
`c
#include "stdlib/stats/base/dists/betaprime/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 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_betaprime_pdf( x, alpha, beta );
printf( "x: %lf, α: %lf, β: %lf, f(x;α,β): %lf\n", x, alpha, beta, 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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[betaprime-distribution]: https://en.wikipedia.org/wiki/Beta_prime_distribution
[pdf]: https://en.wikipedia.org/wiki/Probability_density_function