About stdlib...

We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

gammaincinv

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Inverse of [incomplete gamma function][incomplete-gamma-function].

Computes the inverse of the lower [incomplete gamma function][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:

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

Installation

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

`Usage`

`javascript 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.

`javascript 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.

`javascript 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.

`javascript var y = gammaincinv( 1.2, 1.0 ); // returns NaN

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

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var gammaincinv = require( '@stdlib/math-base-special-gammaincinv' );

var opts = { 'dtype': 'float64' }; var p = uniform( 100, 0.0, 1.0, opts ); var a = uniform( 100, 0.0, 50.0, opts );

logEachMap( 'p: %0.4f, \t a: %0.4f, \t P^(-1)(p, a): %0.4f', p, a, gammaincinv );`

*

`Notice`

This package is part of [stdlib][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][stdlib], see the main project [repository][stdlib].

#### Community

[![Chat][chat-image]][chat-url]

---

`License`

See [LICENSE][stdlib-license].

`Copyright`

[npm-image]: http://img.shields.io/npm/v/@stdlib/math-base-special-gammaincinv.svg [npm-url]: https://npmjs.org/package/@stdlib/math-base-special-gammaincinv

[test-image]: https://github.com/stdlib-js/math-base-special-gammaincinv/actions/workflows/test.yml/badge.svg?branch=v0.2.3 [test-url]: https://github.com/stdlib-js/math-base-special-gammaincinv/actions/workflows/test.yml?query=branch:v0.2.3

[coverage-image]: https://img.shields.io/codecov/c/github/stdlib-js/math-base-special-gammaincinv/main.svg [coverage-url]: https://codecov.io/github/stdlib-js/math-base-special-gammaincinv?branch=main

[chat-image]: https://img.shields.io/badge/zulip-join_chat-brightgreen.svg [chat-url]: https://stdlib.zulipchat.com

[stdlib]: https://github.com/stdlib-js/stdlib

[stdlib-authors]: https://github.com/stdlib-js/stdlib/graphs/contributors

[umd]: https://github.com/umdjs/umd [es-module]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Guide/Modules

[deno-url]: https://github.com/stdlib-js/math-base-special-gammaincinv/tree/deno [deno-readme]: https://github.com/stdlib-js/math-base-special-gammaincinv/blob/deno/README.md [umd-url]: https://github.com/stdlib-js/math-base-special-gammaincinv/tree/umd [umd-readme]: https://github.com/stdlib-js/math-base-special-gammaincinv/blob/umd/README.md [esm-url]: https://github.com/stdlib-js/math-base-special-gammaincinv/tree/esm [esm-readme]: https://github.com/stdlib-js/math-base-special-gammaincinv/blob/esm/README.md [branches-url]: https://github.com/stdlib-js/math-base-special-gammaincinv/blob/main/branches.md

[stdlib-license]: https://raw.githubusercontent.com/stdlib-js/math-base-special-gammaincinv/main/LICENSE

[incomplete-gamma-function]: https://en.wikipedia.org/wiki/Incomplete_gamma_function

[@stdlib/math/base/special/gamma]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma

[@stdlib/math/base/special/gamma1pm1]: https://www.npmjs.com/package/@stdlib/math-base-special-gamma1pm1

[@stdlib/math/base/special/gammainc]: https://www.npmjs.com/package/@stdlib/math-base-special-gammainc

[@stdlib/math/base/special/gammaln]: https://www.npmjs.com/package/@stdlib/math-base-special-gammaln


  
    About stdlib...
  

  We believe in a future in which the web is a preferred environment for numerical computation. To help realize this future, we've built stdlib. stdlib is a standard library, with an emphasis on numerical and scientific computation, written in JavaScript (and C) for execution in browsers and in Node.js.

  The library is fully decomposable, being architected in such a way that you can swap out and mix and match APIs and functionality to cater to your exact preferences and use cases.

  When you use stdlib, you can be absolutely certain that you are using the most thorough, rigorous, well-written, studied, documented, tested, measured, and high-quality code out there.

  To join us in bringing numerical computing to the web, get started by checking us out on GitHub, and please consider financially supporting stdlib. We greatly appreciate your continued support!

`gammaincinv`

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url]

> Inverse of [incomplete gamma function][incomplete-gamma-function].

Computes the inverse of the lower [incomplete gamma function][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`

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

`Usage`

`javascript 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.

`javascript 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.

`javascript 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.

`javascript var y = gammaincinv( 1.2, 1.0 ); // returns NaN

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

`Examples`

`javascript var uniform = require( '@stdlib/random-array-uniform' ); var logEachMap = require( '@stdlib/console-log-each-map' ); var gammaincinv = require( '@stdlib/math-base-special-gammaincinv' );

var opts = { 'dtype': 'float64' }; var p = uniform( 100, 0.0, 1.0, opts ); var a = uniform( 100, 0.0, 50.0, opts );

logEachMap( 'p: %0.4f, \t a: %0.4f, \t P^(-1)(p, a): %0.4f', p, a, gammaincinv ); `