# @stdlib/stats-base-dists-arcsine-logcdf 0.1.0 • Public • Published

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# Logarithm of Cumulative Distribution Function

Arcsine distribution logarithm of cumulative distribution function.

The cumulative distribution function for an arcsine random variable is

where `a` is the minimum support and `b` is the maximum support. The parameters must satisfy `a < b`.

## Installation

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

## Usage

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

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

Evaluates the logarithm of the cumulative distribution function (CDF) for an arcsine distribution with parameters `a` (minimum support) and `b` (maximum support).

```var y = logcdf( 9.0, 0.0, 10.0 );
// returns ~-0.23

y = logcdf( 0.5, 0.0, 2.0 );
// returns ~-1.1

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

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

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

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

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

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

If provided `a >= b`, the function returns `NaN`.

```var y = logcdf( 1.0, 2.5, 2.0 );
// returns NaN```

#### logcdf.factory( a, b )

Returns a function for evaluating the logarithm of the cumulative distribution function of an arcsine distribution with parameters `a` (minimum support) and `b` (maximum support).

```var mylogcdf = logcdf.factory( 0.0, 10.0 );
var y = mylogcdf( 0.5 );
// returns ~-1.941

y = mylogcdf( 8.0 );
// returns ~-0.35```

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

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

for ( i = 0; i < 25; i++ ) {
x = ( randu()*20.0 ) - 10.0;
a = ( randu()*20.0 ) - 20.0;
b = a + ( randu()*40.0 );
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.

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