Logarithm of Probability Density Function

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

The probability density function (PDF) 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-logpdf

Usage

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

logpdf( x, a, b )

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

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

y = logpdf( 0.5, 2.0, 4.0 );
// returns ~0.523

y = logpdf( 0.2, 2.0, 2.0 );
// returns ~-0.264

y = logpdf( 0.8, 4.0, 4.0 );
// returns ~0.522

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

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

y = logpdf( 1.5, 4.0, 2.0 );
// returns -Infinity

y = logpdf( +Infinity, 4.0, 2.0 );
// 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 a <= 0, the function returns NaN.

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

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

If provided b <= 0, the function returns NaN.

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

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

logpdf.factory( a, b )

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

var mylogpdf = logpdf.factory( 0.5, 0.5 );

var y = mylogpdf( 0.8 );
// returns ~-0.151

y = mylogpdf( 0.3 );
// returns ~-0.388

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-kumaraswamy-logpdf' );

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 = logpdf( 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.

Community

License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.