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# betaincinv

Beta inverse cumulative distribution function

## Syntax

x = betaincinv(y,z,w)
x = betaincinv(y,z,w,tail)

## Description

x = betaincinv(y,z,w) computes the inverse incomplete beta function for corresponding elements of y, z, and w, such that y = betainc(x,z,w). The elements of y must be in the closed interval [0,1], and those of z and w must be nonnegative. y, z, and w must all be real and the same size (or any of them can be scalar).

x = betaincinv(y,z,w,tail) specifies the tail of the incomplete beta function. Choices are 'lower' (the default) to use the integral from 0 to x, or 'upper' to use the integral from x to 1. These two choices are related as follows: betaincinv(y,z,w,'upper') = betaincinv(1-y,z,w,'lower'). When y is close to 0, the 'upper' option provides a way to compute x more accurately than by subtracting y from 1.

## Definitions

The incomplete beta function is defined as

${I}_{x}\left(z,w\right)=\frac{1}{\beta \left(z,w\right)}\underset{0}{\overset{x}{\int }}{t}^{\left(z-1\right)}{\left(1-t\right)}^{\left(w-1\right)}dt$

betaincinv computes the inverse of the incomplete beta function with respect to the integration limit x using Newton's method.