[R] parameter estimation

[Douglas Bates]

Vittorio Addona <vaddon at po-box.mcgill.ca> writes:

> Hello, my question is the following: from a data set (assuming the data
> has a parametric form, gamma, say) how can I estimate the parameters of
> the data's density.  That is,
> for the gamma, say, how can I estimate alpha and beta using R?  Thank
> you.

One possibility is to use maximum likelihood, which is surprisingly
easy to implement in R.  The log-likelihood function for the parameters
alpha and beta given the data x is
  sum(dgamma(x, shape = alpha, scale = beta, log = TRUE))
To determine the maximum likelihood estimates, simply put the negative
of the log-likelihood into the optim function.

A worked-out example is given as xmp06.12 in the Devore5 library
(available in the contrib section at CRAN).  Use

 library(Devore5)
 help(xmp06.12)      # shows the description with comments
 example(xmp06.12)   # run the example to see the result

That example also shows the calculations for the method of moments
estimators but I would not recommend them.
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