Re: New book: Statistics - A Maxima Companion

Wolfgang, a few more thoughts about statistics with Maxima.

Another context in which the symbolic and numerical aspects intersect
is in parameter estimation. Very generally, a conventional approach is
to construct a likelihood function and then look for parameter values
which maximize the likelihood. A likelihood function is very easily
constructed as something along the lines of

  L: product (pdf_something (x[k], param1, param2, ...), k, 1, length (x));

where x is a list of values (typically but not necessarily numeric)
and pdf_something is some specific density function with parameters
param1, param2, etc. For example

  x: [ 11, 13, 29, 17, 19, 23, 4, 7 ];
  L: product (pdf_normal (x[k], mu, sigma), k, 1, length (x));

and then looking at log(L) with logexpand = true, contour plots of
log(L), looking at partial derivatives, verifying that the minimum of
log(L) coincides with the sample mean and standard deviation, etc.

I first got interested in Maxima because I was trying to compute
survival functions for some kinds of parametric survival models; the
survival function is defined in terms of an integral, and I had
reached the limit of what I could do with pencil and paper. It is a
specialized topic, but anyway parametric survival models are a "neat"
application of computer algebra, as several quantities of interest are
defined, starting from a hazard function, i.e., p(T in interval [ t, t
+ dt ] given T > t) where T is the time of death or failure.

Likewise one could start with a pdf and derive the cdf, expected
value, moments, etc. in terms of the pdf via whatever integrals are
needed. That could be a win for, let's say, distributions defined
piecewise or otherwise clumsy to handle with pencil and paper.

Finally, one could generate code for some derived function, suitable
to be pasted into another program, Python, C/C++, etc.

Just some ideas here, I've never gotten around writing this stuff down
and working out the details, maybe someday.

All the best,

Robert