Inversed incomplete Beta function

Evaluates the inverse of the incomplete beta function

The incomplete beta function is defined as

\mathrm{B}(x; a, b) = \int_0^x t^{a-1}(1-t)^{b-1}\,\mathrm{d}t

The regularized incomplete beta function (or regularized beta function for short) is defined in terms of the incomplete beta function and the complete beta function:

\mathrm{I}_{x}(a, b) = \dfrac{\mathrm{B}(x; a, b)}{\mathrm{B}(a, b)}

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

Installation

$ npm install @toshiara/special-betaincinv

Usage

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

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

betaincinv(p, a, b[, option])

Inverts the regularized incomplete beta function.

Contrary to the more commonly used definition, in this implementation the first parameter is the probability p and the second and third parameter are a and b.

The function accepts the following option:

• upper:boolean indicating whether to evaluate the lower (false) or upper (true) incomplete beta function. Default: false.

// lower
betaincinv(0.001, 1.1, 2);
// returns 0.0009549886032748866

betaincinv(0.1, 1, 2)
// returns 0.0513167019494862

betaincinv(0.4, 1.5, 2.5)
// returns 0.2904180852037441

betaincinv(0.8, 3, 4)
// returns 0.5853942353021732

betaincinv(0.999, 4.5, 3.5)
// returns 0.9485177162846162


// upper
betaincinv(0.001, 1.1, 2, { upper: true });
// returns 0.9990450113967251

betaincinv(0.1, 1, 2, { upper: true })
// returns 0.9486832980505138

betaincinv(0.4, 1.5, 2.5, { upper: true })
// returns 0.7095819147962559

betaincinv(0.8, 3, 4, { upper: true })
// returns 0.41460576469782684

betaincinv(0.999, 4.5, 3.5, { upper: true })
// returns 0.05148228371538377

License

MIT license.