# 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```