Colin Rose

Symbolic Maximum Likelihood Estimation with Mathematica

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 Mathematicas ability to simplify expressions involving the natural logarithm of a product of algebraic terms. This enhancement to Mathematicas functionality can be of particular benefit for maximum likelihood estimation.

mathStatica: Mathematical Statistics with Mathematica

This paper presents mathStatica (2002), a completely general toolset for doing mathematical statistics with Mathematica (Version 4). mathStatica defines statistical operators for taking expectations, finding probabilities, deriving transformations of random variables and so on. Importantly, mathStatica is not tied to a set of pre-specified statistical distributions. Rather, it is designed to derive statistics such as moments, cumulative distribution functions, characteristic functions, and other generating functions for user-defined distributions. mathStatica supports discrete and continuous distributions — univariate and multivariate. Applications to inference include: estimation (moment unbiased, minimum variance unbiased, best unbiased, maximum likelihood: symbolic and numeric), curve-fitting (Pearson and Johnson systems, non-parametric kernels), asymptotics, decision theory, and moment conversion formulae (for conversion between cumulants, raw moments, and central moments: univariate and multivariate). mathStatica accompanies the book: Rose and Smith (2002), Mathematical Statistics with Mathematica (Springer Texts in Statistics).