Beta probability density function
Y = betapdf(X,A,B)
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
where B( · ) is the Beta function. The indicator function 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.
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