Regularized incomplete Beta function

Evaluates the regularized 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 ibeta function in jstat in Typescript. This package supports both CommonJs and ES Modules.

Installation

$ npm install @toshiara/special-betainc

Usage

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

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

betainc(x, a, b[, option])

Evaluates the regularized lower or upper incomplete beta function for inputs x, a > 0 and b > 0.

The function accepts the following option:

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

// regularized lower incomplete beta function
betainc(0.001, 1.1, 2);
// returns 0.001051941884660282

betainc(0.1, 1, 2)
// returns 0.18999999999999992

betainc(0.4, 1.5, 2.5)
// returns 0.5731324201681518

betainc(0.8, 3, 4)
// returns 0.98304

betainc(0.999, 4.5, 3.5)
// returns 0.9999999988252123

// regularized upper incomplete beta function
betainc(0.4, 1.5, 2.5, { upper: true })
// returns 0.4268675798318482

License

MIT license.