Probability Density Function

Arcsine distribution probability density function (PDF).

The probability density function (PDF) for an arcsine random variable is

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

Installation

npm install @stdlib/stats-base-dists-arcsine-pdf

Usage

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

pdf( x, a, b )

Evaluates the probability density function (PDF) for an arcsine distribution with parameters a (minimum support) and b (maximum support).

var y = pdf( 2.0, 0.0, 4.0 );
// returns ~0.159

y = pdf( 5.0, 0.0, 4.0 );
// returns 0.0

y = pdf( 0.25, 0.0, 1.0 );
// returns ~0.735

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

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

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

y = pdf( 0.0, 0.0, NaN );
// returns NaN

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

var y = pdf( 2.5, 3.0, 2.0 );
// returns NaN

y = pdf( 2.5, 3.0, 3.0 );
// returns NaN

pdf.factory( a, b )

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

var myPDF = pdf.factory( 6.0, 7.0 );
var y = myPDF( 7.0 );
// returns Infinity

y = myPDF( 5.0 );
// returns 0.0

Examples

var randu = require( '@stdlib/random-base-randu' );
var pdf = require( '@stdlib/stats-base-dists-arcsine-pdf' );

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 = pdf( x, a, b );
    console.log( 'x: %d, a: %d, b: %d, 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.