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# betapdf

Beta probability density function

## Syntax

Y = betapdf(X,A,B)

## Description

Y = betapdf(X,A,B) computes the beta pdf at each of the values in X using the corresponding parameters in A and B. X, A, and B can be vectors, matrices, or multidimensional arrays that all have the same size. A scalar input is expanded to a constant array with the same dimensions of the other inputs. The parameters in A and B must all be positive, and the values in X must lie on the interval [0, 1].

The beta probability density function for a given value x and given pair of parameters a and b is

$y=f\left(x|a,b\right)=\frac{1}{B\left(a,b\right)}{x}^{a-1}{\left(1-x\right)}^{b-1}{I}_{\left(0,1\right)}\left(x\right)$

where B( · ) is the Beta function. The indicator function ${I}_{\left(0,1\right)}\left(x\right)$ ensures that only values of x in the range (0 1) have nonzero probability. The uniform distribution on (0 1) is a degenerate case of the beta pdf where a = 1 and b = 1.

A likelihood function is the pdf viewed as a function of the parameters. Maximum likelihood estimators (MLEs) are the values of the parameters that maximize the likelihood function for a fixed value of x.

## Examples

```a = [0.5 1; 2 4]
a =
0.5000  1.0000
2.0000  4.0000
y = betapdf(0.5,a,a)
y =
0.6366  1.0000
1.5000  2.1875```