Neoclassical Programming Multitude

    @stdlib/stats-base-dists-cauchy-logcdf
    TypeScript icon, indicating that this package has built-in type declarations

    0.0.5 • Public • Published

    Logarithm of Cumulative Distribution Function

    NPM version Build Status Coverage Status dependencies

    Cauchy distribution logarithm of cumulative distribution function.

    The cumulative distribution function for a Cauchy random variable is

    Cumulative distribution function for a Cauchy distribution.

    where x0 is the location parameter and gamma > 0 is the scale parameter.

    Installation

    npm install @stdlib/stats-base-dists-cauchy-logcdf

    Usage

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

    logcdf( x, x0, gamma )

    Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Cauchy distribution with parameters x0 (location parameter) and gamma > 0 (scale parameter).

    var y = logcdf( 4.0, 0.0, 2.0 );
    // returns ~-0.16
    
    y = logcdf( 1.0, 0.0, 2.0 );
    // returns ~-0.435
    
    y = logcdf( 1.0, 3.0, 2.0 );
    // returns ~-1.386

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

    var y = logcdf( NaN, 0.0, 2.0 );
    // returns NaN
    
    y = logcdf( 1.0, 2.0, NaN );
    // returns NaN
    
    y = logcdf( 1.0, NaN, 3.0 );
    // returns NaN

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

    var y = logcdf( 2.0, 0.0, -1.0 );
    // returns NaN
    
    y = logcdf( 2.0, 0.0, 0.0 );
    // returns NaN

    logcdf.factory( x0, gamma )

    Returns a function for evaluating the natural logarithm of the cumulative distribution function of a Cauchy distribution with parameters x0 (location parameter) and gamma > 0 (scale parameter).

    var mylogcdf = logcdf.factory( 10.0, 2.0 );
    
    var y = mylogcdf( 10.0 );
    // returns ~-0.693
    
    y = mylogcdf( 12.0 );
    // returns ~-0.288

    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-cauchy-logcdf' );
    
    var gamma;
    var x0;
    var x;
    var y;
    var i;
    
    for ( i = 0; i < 10; i++ ) {
        x = randu() * 10.0;
        x0 = randu() * 10.0;
        gamma = ( randu()*10.0 ) + EPS;
        y = logcdf( x, x0, gamma );
        console.log( 'x: %d, x0: %d, γ: %d, ln(F(x;x0,γ)): %d', x, x0, gamma, y );
    }

    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

    Chat


    License

    See LICENSE.

    Copyright

    Copyright © 2016-2021. The Stdlib Authors.

    Install

    npm i @stdlib/stats-base-dists-cauchy-logcdf

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    15

    Version

    0.0.5

    License

    Apache-2.0

    Unpacked Size

    57.8 kB

    Total Files

    11

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser