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).