# betacdf

Beta cumulative distribution function

## Syntax

`p = betacdf(x,a,b)p = betacdf(x,a,b,'upper')`

## Description

`p = betacdf(x,a,b)` returns the beta cdf 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 as 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].

`p = betacdf(x,a,b,'upper')` returns the complement of the beta cdf at each of the values in `x`, using an algorithm that more accurately computes the extreme upper tail probabilities.

The beta cdf for a given value `x` and given pair of parameters `a` and `b` is

$p=F\left(x|a,b\right)=\frac{1}{B\left(a,b\right)}\underset{0}{\overset{x}{\int }}{t}^{a-1}{\left(1-t\right)}^{b-1}dt$

where B( · ) is the Beta function.

## Examples

collapse all

### Compute Beta Distribution CDF

Compute the cdf for a beta distribution with parmaters ```a = 2``` and `b = 2`.

```x = 0.1:0.2:0.9; a = 2; b = 2; p = betacdf(x,a,b)```
```p = 0.0280 0.2160 0.5000 0.7840 0.9720 ```
```a = [1 2 3]; p = betacdf(0.5,a,a) ```
```p = 0.5000 0.5000 0.5000```