# 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