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

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

where B( · ) is the Beta function. 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

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using MATLAB® Coder™.

GPU Arrays

Accelerate code by running on a graphics processing unit (GPU) using Parallel Computing Toolbox™.

This function fully supports GPU arrays. For more information, see Run MATLAB Functions on a GPU (Parallel Computing Toolbox).

Version History

Introduced before R2006a