Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

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)=1B(a,b)xa1(1x)b1I[0,1](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

Introduced before R2006a

Was this topic helpful?