Core Algorithms
Probability and statistics solvers and Properties

Building on two decades of development in symbolic and numeric algorithms, Mathematica 8 provides a suite of high-level functions for probability and statistics. New capabilities, including the ability to compute the probability of any event or the expectation of any expression, simulate any distribution, and automatically estimate parameters or test goodness of fit for distributions. To support distributional modeling and analysis, Mathematica 8 offers the largest collection of probability distributions, as well as full support for several dozens of properties, including distribution functions, moments, quantiles, and generating functions.

Symbolic and numeric computation of probabilities and conditional probabilities of events as logical combinations of equations and inequalities. »

Symbolic and numeric computation of expectations and conditional expectations of expressions. »

Typeset characters for distributed () and conditioned (). »

Automatic support for simulating distributions, estimating parameters in distributions, and testing goodness-of-fit for distributions. »

Direct support for several different distribution functions including PDF, CDF, survival, hazard, inverse CDF, and inverse survival functions. »

Direct support for several different types of moments including raw moments, central moments, cumulants, and factorial moments. »

Direct support for all the generating functions associated with moments, including moment-generating functions and cumulant-generating functions. »

Automatic conversion from between different types of moments. »

Automatic computation of standard and unbiased moment estimators. »

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