gammincinv

Inverse of incomplete gamma function.

Computes the inverse of the 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:

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 ) );
}

See Also

• @stdlib/math-base/special/gamma: gamma function.
• @stdlib/math-base/special/gamma1pm1: compute gamma(x+1) - 1.
• @stdlib/math-base/special/gammainc: incomplete gamma function.
• @stdlib/math-base/special/gammaln: natural logarithm of the gamma function.

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.