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

0.2.1 • Public • Published

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!

# Logarithm of Cumulative Distribution Function

Evaluate the natural logarithm of the cumulative distribution function for a beta prime distribution .

The cumulative distribution function for a beta prime random variable is

where `alpha > 0` is the first shape parameter, `beta > 0` is the second shape parameter and `I` is the incomplete beta function.

## Installation

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

## Usage

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

#### logcdf( x, alpha, beta )

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

```var y = logcdf( 0.5, 1.0, 1.0 );
// returns ~-1.099

y = logcdf( 0.5, 2.0, 4.0 );
// returns ~-0.618

y = logcdf( 0.2, 2.0, 2.0 );
// returns ~-2.603

y = logcdf( 0.8, 4.0, 4.0 );
// returns ~-0.968

y = logcdf( -0.5, 4.0, 2.0 );
// returns -Infinity

y = logcdf( +Infinity, 4.0, 2.0 );
// returns 0.0```

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

```var y = logcdf( NaN, 1.0, 1.0 );
// returns NaN

y = logcdf( 0.0, NaN, 1.0 );
// returns NaN

y = logcdf( 0.0, 1.0, NaN );
// returns NaN```

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

```var y = logcdf( 2.0, -1.0, 0.5 );
// returns NaN

y = logcdf( 2.0, 0.0, 0.5 );
// returns NaN```

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

```var y = logcdf( 2.0, 0.5, -1.0 );
// returns NaN

y = logcdf( 2.0, 0.5, 0.0 );
// returns NaN```

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

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

```var mylogcdf = logcdf.factory( 0.5, 0.5 );

var y = mylogcdf( 0.8 );
// returns ~-0.767

y = mylogcdf( 0.3 );
// returns ~-1.143```

## 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 logcdf = require( '@stdlib/stats-base-dists-betaprime-logcdf' );

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 = logcdf( 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-logcdf`

stdlib.io

66

0.2.1

Apache-2.0

54.8 kB

13