Notify President Madagascar

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

    0.0.7 • Public • Published

    Logarithm of Cumulative Distribution Function

    NPM version Build Status Coverage Status

    Evaluate the natural logarithm of the cumulative distribution function (CDF) for a Student's t distribution.

    The cumulative distribution function (CDF) for a t distribution random variable is

    Cumulative distribution function (CDF) for a Student's t distribution.

    where v > 0 is the degrees of freedom. In the definition, Beta( x; a, b ) denotes the lower incomplete beta function and Beta( a, b ) the beta function.

    Installation

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

    Usage

    var logcdf = require( '@stdlib/stats-base-dists-t-logcdf' );

    logcdf( x, v )

    Evaluates the natural logarithm of the cumulative distribution function (CDF) for a Student's t distribution with degrees of freedom v.

    var y = logcdf( 2.0, 0.1 );
    // returns ~-0.493
    
    y = logcdf( 1.0, 2.0 );
    // returns ~-0.237
    
    y = logcdf( -1.0, 4.0 );
    // returns ~-1.677

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

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

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

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

    logcdf.factory( v )

    Returns a function for evaluating the natural logarithm of the CDF of a Student's t distribution with degrees of freedom v.

    var mylogcdf = logcdf.factory( 0.5 );
    var y = mylogcdf( 3.0 );
    // returns ~-0.203
    
    y = mylogcdf( 1.0 );
    // returns ~-0.358

    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-t-logcdf' );
    
    var v;
    var x;
    var y;
    var i;
    
    for ( i = 0; i < 10; i++ ) {
        x = (randu() * 6.0) - 3.0;
        v = randu() * 10.0;
        y = logcdf( x, v );
        console.log( 'x: %d, v: %d, ln(F(x;v)): %d', x.toFixed( 4 ), v.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

    Chat


    License

    See LICENSE.

    Copyright

    Copyright © 2016-2022. The Stdlib Authors.

    Install

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

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    94

    Version

    0.0.7

    License

    Apache-2.0

    Unpacked Size

    43.6 kB

    Total Files

    11

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser