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betainv

Beta inverse cumulative distribution function

Syntax

X = betainv(P,A,B)

Description

X = betainv(P,A,B) computes the inverse of the beta cdf with parameters specified by A and B for the corresponding probabilities in P. P, A, and B can be vectors, matrices, or multidimensional arrays that are all the same size. A scalar input is expanded to a constant array with the same dimensions as the other inputs. The parameters in A and B must all be positive, and the values in P must lie on the interval [0, 1].

The inverse beta cdf for a given probability p and a given pair of parameters a and b is

x=F1(p|a,b)={x:F(x|a,b)=p}

where

p=F(x|a,b)=1B(a,b)0xta1(1t)b1dt

and B( · ) is the Beta function. Each element of output X is the value whose cumulative probability under the beta cdf defined by the corresponding parameters in A and B is specified by the corresponding value in P.

Examples

p = [0.01 0.5 0.99];
x = betainv(p,10,5)
x =
  0.3726  0.6742  0.8981

According to this result, for a beta cdf with a = 10 and b = 5, a value less than or equal to 0.3726 occurs with probability 0.01. Similarly, values less than or equal to 0.6742 and 0.8981 occur with respective probabilities 0.5 and 0.99.

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Algorithms

The betainv function uses Newton's method with modifications to constrain steps to the allowable range for x, i.e., [0 1].

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