betainv (Statistics Toolbox)

Inverse of the beta cumulative distribution function.

Syntax

X = betainv(P,A,B)

Description

betainv(P,A,B) computes the inverse of the beta cdf with parameters A and B for the probabilities in P. The arguments P, A, and B must all be the same size except that scalar arguments function as constant matrices of the common size of the other arguments.

The parameters A and B must both be positive and P must lie on the interval
[0 1].

The beta inverse function in terms of the beta cdf is:

where

The result, x, is the solution of the integral equation of the beta cdf with parameters a and b where you supply the desired probability p.

Algorithm

We use Newton's Method with modifications to constrain steps to the allowable range for x, i.e., [0 1].

Examples

p = [0.01 0.5 0.99];
x = betainv(p,10,5)

x =

    0.3726    0.6742    0.8981

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