"Symbolic Maximum Likelihood Estimation with Mathematica"

COLIN ROSE 
Theoretical Research Institute, Sydney, Australia
and MURRAY D. SMITH* 
Department of Econometrics, University of Sydney, Sydney, Australia


Mathematica is a symbolic programming language that empowers the user to 
undertake complicated algebraic tasks. One such task is the derivation of 
maximum likelihood estimators, demonstrably an important topic in statistics at 
both the research and expository level. In this paper, a Mathematica package 
is provided that contains a function entitled SuperLog. This function utilises 
pattern-matching code that enhances Mathematica's ability to simplify 
expressions involving the natural logarithm of a product of algebraic terms. 
This enhancement to Mathematica's functionality can be of particular benefit 
for maximum likelihood estimation.