betalike
Beta negative log-likelihood
Syntax
nlogL = betalike(params,data)
[nlogL,AVAR] = betalike(params,data)
Description
nlogL = 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 the column vector data.
The elements of data must lie in the open
interval (0, 1), where the beta distribution is defined. However,
it is sometimes also necessary to fit a beta distribution to data
that include exact zeros or ones. For such data, the beta likelihood
function is unbounded, and standard maximum likelihood estimation
is not possible. In that case, betalike computes
a modified likelihood that incorporates the zeros or ones by treating
them as if they were values that have been left-censored at sqrt(realmin) or
right-censored at 1-eps/2, respectively.
[nlogL,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.
Examples
This example continues the betafit example,
which calculates estimates of the beta parameters for some randomly
generated beta distributed data.
r = betarnd(4,3,100,1);
[nlogl,AVAR] = betalike(betafit(r),r)
nlogl =
-27.5996
AVAR =
0.2783 0.1316
0.1316 0.0867Extended Capabilities
Version History
Introduced before R2006a
