Statistics Toolbox

betalike

Negative beta log-likelihood function

Syntax

• logL = betalike(params,data)
  [logL,avar] = betalike(params,data)
  

Description

logL = betalike(params,data) returns the negative of the beta log-likelihood function for the beta parameters a and b specified in vector params and the observations specified in column vector data. The length of logL is the length of data.

[logL,avar] = betalike(params,data) also returns avar, which is the asymptotic variance-covariance matrix of the parameter estimates if the values in params are the maximum likelihood estimates. avar is the inverse of Fisher's information matrix. The diagonal elements of avar are the asymptotic variances of their respective parameters.

betalike is a utility function for maximum likelihood estimation of the beta distribution. The likelihood assumes that all the elements in the data sample are mutually independent. Since betalike returns the negative beta log-likelihood function, minimizing betalike using fminsearch is the same as maximizing the likelihood.

Example

This example continues the betafit example where we calculated estimates of the beta parameters for some randomly generated beta distributed data.

• r = betarnd(4,3,100,1);
  [logl,avar] = betalike([3.9010 2.6193],r)
  logl =
    -33.0514
  avar =
      0.2856    0.1528
      0.1528    0.1142
  

See Also
betafit, fminsearch, gamlike, mle, normlike, weiblike

betainv

betapdf