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We present a unified approach for doing mathematical statistics with Mathematica. At one extreme, our package PDF empowers even the "statistically challenged" with the ability to perform complicated operations without even realizing it. At the other extreme, it enables the professional statistician to tackle tricky multivariate distributions, generating functions, inversion theorems, symbolic MLE, unbiased estimation, checking (and correcting) of textbook formulas, and so on. Features include: a suite of functions for manipulating pdfs, symbolic maximum likelihood estimation (a world first), numerical MLE (now augments FindMinimum with standard error output), automated Pearson curve fitting (normally very tricky), and also Johnson fitting, Gram-Charlier expansions, nonparametric kernel density estimation, moment conversion formulas (convert automatically between cumulants, raw moments, central moments, and factorial moments--univariate and multivariate!), random number generation for any discrete distribution, automated transformations (functions of random variables), asymptotics (symbolic proofs), decision theory (order statistics, mean square error, etc.), and unbiased estimation (h-statistics, k-statistics, polykays). The package replaces dozens of reference works and extends the analysis for the first time to problems of arbitrary high order.
The above forms the basis of a Springer-Verlag text entitled Mathematical Statistics with Mathematica (500 pages) that will ship with CD-ROM, custom Mathematica 3 palettes, online help, and live interactive chapters, providing a simple and unified approach for doing mathematical statistics with Mathematica. The session will be of multidisciplinary interest since mathematical statistics is used not only by statisticians but also by economists, engineers, and physicists--indeed, across the full ambit of the physical/social sciences and across both the pure and the applied domains.
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