npm package: @stdlib/stats-base-dists-betaprime-logcdf
Description: Evaluate the natural logarithm of the cumulative distribution function (CDF) for a beta prime distribution.
Author: The Stdlib Authors
Latest version: 0.2.3

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# Logarithm of Cumulative Distribution Function

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> Evaluate the natural logarithm of the [cumulative distribution function][cdf] for a [beta prime][betaprime-distribution] distribution.

<section class="intro">

The [cumulative distribution function][cdf] for a [beta prime][betaprime-distribution] random variable is

<!-- <equation class="equation" label="eq:betaprime_cdf" align="center" raw="F(x;\alpha,\beta) = \begin{cases} I_{\frac{x}{1+x}}(\alpha, \beta) & \text{ for } x > 0 \\ 0 & \text{ otherwise } \end{cases}" alt="Cumulative distribution function for a beta prime distribution."> -->

<div class="equation" align="center" data-raw-text="F(x;\alpha,\beta) = \begin{cases} I_{\frac{x}{1+x}}(\alpha, \beta) &amp; \text{ for } x &gt; 0 \\ 0 &amp; \text{ otherwise } \end{cases}" data-equation="eq:betaprime_cdf">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@51534079fef45e990850102147e8945fb023d1d0/lib/node_modules/@stdlib/stats/base/dists/betaprime/logcdf/docs/img/equation_betaprime_cdf.svg" alt="Cumulative distribution function for a beta prime distribution.">
    <br>
</div>

<!-- </equation> -->

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

</section>

<!-- /.intro -->

<section class="installation">

## Installation

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

</section>

<section class="usage">

## Usage

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

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

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

```javascript
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`.

```javascript
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`.

```javascript
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`.

```javascript
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][cdf] for a [beta prime][betaprime-distribution] distribution with parameters `alpha` (first shape parameter) and `beta` (second shape parameter).

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

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

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

</section>

<!-- /.usage -->

<section class="notes">

## 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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var uniform = require( '@stdlib/random-array-uniform' );
var logEachMap = require( '@stdlib/console-log-each-map' );
var EPS = require( '@stdlib/constants-float64-eps' );
var logcdf = require( '@stdlib/stats-base-dists-betaprime-logcdf' );

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, ln(F(x;α,β)): %0.4f', x, alpha, beta, logcdf );
```

</section>

<!-- /.examples -->

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<section class="related">

</section>

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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].

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## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[betaprime-distribution]: https://en.wikipedia.org/wiki/Beta_prime_distribution

[cdf]: https://en.wikipedia.org/wiki/Cumulative_distribution_function

[incomplete-beta]: https://en.wikipedia.org/wiki/Beta_function#Incomplete_beta_function

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