# @stdlib/stats-base-dists-betaprime-logpdf

0.1.0 • Public • Published

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# Logarithm of Probability Density Function

Beta prime distribution logarithm of probability density function (PDF).

The probability density function (PDF) for a beta prime random variable is

where `α > 0` is the first shape parameter and `β > 0` is the second shape parameter.

## Installation

`npm install @stdlib/stats-base-dists-betaprime-logpdf`

## Usage

`var logpdf = require( '@stdlib/stats-base-dists-betaprime-logpdf' );`

#### logpdf( x, alpha, beta )

Evaluates the natural logarithm of the probability density function (PDF) for a beta prime distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).

```var y = logpdf( 0.5, 0.5, 1.0 );
// returns ~-0.955

y = logpdf( 0.1, 1.0, 1.0 );
// returns ~-0.191

y = logpdf( 0.8, 4.0, 2.0 );
// returns ~-1.2```

If provided an input value `x` outside smaller or equal to zero, the function returns `-Infinity`.

```var y = logpdf( -0.1, 1.0, 1.0 );
// returns -Infinity```

If provided `NaN` as any argument, the function returns `NaN`.

```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 NaN```

If provided `alpha <= 0`, the function returns `NaN`.

```var y = logpdf( 0.5, 0.0, 1.0 );
// returns NaN

y = logpdf( 0.5, -1.0, 1.0 );
// returns NaN```

If provided `beta <= 0`, the function returns `NaN`.

```var y = logpdf( 0.5, 1.0, 0.0 );
// returns NaN

y = logpdf( 0.5, 1.0, -1.0 );
// returns NaN```

#### logpdf.factory( alpha, beta )

Returns a `function` for evaluating the natural logarithm of the PDF for a beta prime distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).

```var mylogPDF = logpdf.factory( 0.5, 0.5 );

var y = mylogPDF( 0.8 );
// returns ~-1.62

y = mylogPDF( 0.3 );
// returns ~-0.805```

## 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

```var randu = require( '@stdlib/random-base-randu' );
var EPS = require( '@stdlib/constants-float64-eps' );
var logpdf = require( '@stdlib/stats-base-dists-betaprime-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 ) );
}```

## Notice

This package is part of 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, see the main project repository.

## Package Sidebar

### Install

`npm i @stdlib/stats-base-dists-betaprime-logpdf`

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