@stdlib/math-base-special-gammaincinv
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    gammincinv

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    Inverse of incomplete gamma function.

    Computes the inverse of the lower incomplete gamma function

    Regularized lower incomplete gamma function.

    Specifically, for given p and a it finds the x such that p = P(x, a).

    The function can also be used to invert the upper incomplete gamma function, which is defined as follows:

    Regularized upper incomplete gamma function.

    Again, for given p and a the function returns the x which satisfies p = Q(x, a).

    Installation

    npm install @stdlib/math-base-special-gammaincinv

    Usage

    var gammaincinv = require( '@stdlib/math-base-special-gammaincinv' );

    gammaincinv( p, s[, upper ] )

    Inverts the regularized incomplete gamma function. Contrary to the more commonly used definition, in this implementation the first argument is the probability p and the second argument is the scale factor a. By default, the function inverts the lower regularized incomplete gamma function, P(x,a). To invert the upper function instead, i.e. Q(x,a), set the upper argument to true.

    var y = gammaincinv( 0.5, 2.0 );
    // returns ~1.678
    
    y = gammaincinv( 0.1, 10.0 );
    // returns ~6.221
    
    y = gammaincinv( 0.75, 3.0 );
    // returns ~3.92
    
    y = gammaincinv( 0.75, 3.0, true );
    // returns ~1.727

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

    var y = gammaincinv( NaN, 1.0 );
    // returns NaN
    
    y = gammaincinv( 0.5, NaN );
    // returns NaN

    If provided a value outside [0,1] for p, the function returns NaN.

    var y = gammaincinv( 1.2, 1.0 );
    // returns NaN
    
    y = gammaincinv( -0.5, 1.0 );
    // returns NaN

    Examples

    var randu = require( '@stdlib/random-base-randu' );
    var gammaincinv = require( '@stdlib/math-base-special-gammaincinv' );
    
    var a;
    var i;
    var p;
    
    for ( i = 0; i < 100; i++ ) {
        p = randu();
        a = randu() * 50.0;
        console.log( 'p: %d, \t a: %d, \t P^(-1)(p, a): %d', p.toFixed( 4 ), a.toFixed( 4 ), gammaincinv( p, a ).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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    License

    See LICENSE.

    Copyright

    Copyright © 2016-2021. The Stdlib Authors.

    Install

    npm i @stdlib/math-base-special-gammaincinv

    Homepage

    stdlib.io

    DownloadsWeekly Downloads

    474

    Version

    0.0.5

    License

    Apache-2.0

    Unpacked Size

    110 kB

    Total Files

    33

    Last publish

    Collaborators

    • stdlib-bot
    • kgryte
    • planeshifter
    • rreusser