betainv (Statistics Toolbox)

Inverse of the beta 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. Vector or matrix inputs for P, A, and B must all have the same size. A scalar input is expanded to a constant matrix 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

where

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.

Algorithm

The betainv function uses 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

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.

See Also
betafit, icdf

betafit betalike