# npm

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

0.0.7 • Public • Published

# Logarithm of Cumulative Distribution Function

Evaluate the natural logarithm of the cumulative distribution function for a Kumaraswamy's double bounded distribution.

The cumulative distribution function for a Kumaraswamy's double bounded random variable is

where `a > 0` is the first shape parameter and `b > 0` is the second shape parameter.

## Installation

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

## Usage

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

#### logcdf( x, a, b )

Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Kumaraswamy's double bounded distribution with parameters `a` (first shape parameter) and `b` (second shape parameter).

```var y = logcdf( 0.5, 1.0, 1.0 );
// returns ~-0.693

y = logcdf( 0.5, 2.0, 4.0 );
// returns ~-0.38

y = logcdf( 0.2, 2.0, 2.0 );
// returns ~-2.546

y = logcdf( 0.8, 4.0, 4.0 );
// returns ~-0.13

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

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

y = logcdf( 1.5, 4.0, 2.0 );
// returns 0.0

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 `a <= 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 `b <= 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( a, b )

Returns a function for evaluating the natural logarithm of the cumulative distribution function for a Kumaraswamy's double bounded distribution with parameters `a` (first shape parameter) and `b` (second shape parameter).

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

var y = mylogcdf( 0.8 );
// returns ~-0.393

y = mylogcdf( 0.3 );
// returns ~-1.116```

## 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-kumaraswamy-logcdf' );

var a;
var b;
var x;
var y;
var i;

for ( i = 0; i < 10; i++ ) {
x = randu();
a = ( randu()*5.0 ) + EPS;
b = ( randu()*5.0 ) + EPS;
y = logcdf( x, a, b );
console.log( 'x: %d, a: %d, b: %d, ln(F(x;a,b)): %d', x.toFixed( 4 ), a.toFixed( 4 ), b.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.

### Install

`npm i @stdlib/stats-base-dists-kumaraswamy-logcdf`

stdlib.io

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