gammaincinv

Inverse incomplete gamma function.

This package is a rewrite of jstat in Typescript. This package supports both CommonJs and ES Modules.

Computes the inverse of the lower incomplete gamma function

P( x, a ) = \frac{\gamma(a,x)}{\Gamma(a)} = \frac{1}{\Gamma(a)} \int_0^x t^{a-1} e^{-t} \; dt

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:

Q( x, a ) = \frac{\Gamma(a,x)}{\Gamma(a)} = \frac{1}{\Gamma(a)} \int_x^\infty t^{a-1} e^{-t} \; dt

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

Installation

$ npm install @toshiara/special-gammaincinv

Usage

// for CommonJs
const { gammaincinv } = require('@toshiara/special-gammaincinv');

// for ES Modules
import { gammaincinv } from '@toshiara/special-gammaincinv';

gammaincinv(p, a)

Inverts the regularized incomplete gamma function. Contrary to the more commonly used definitoon, in this implementation the first argument is p and the second argument is the scale factor a.

gammaincinv(0.0001, 2);
// returns 0.014209237621777502

gammaincinv(0.1, 1);
// returns 0.10536051565782636

gammaincinv(0.5, 5);
// returns 4.670908882795985

gammaincinv(0.8, 7);
// returns 9.07538528120425

gammaincinv(0.999, 9);
// returns 21.15619816583997