Technical Description

RiskQ 4.2 is a computer language designed to facilitate quantitative investigations involving probability, uncertainty, and elementary statistics for Mathematica.

RiskQ supports numerous continuous and discontinuous probability distributions, including user-supplied empirical ones. These may be operated on by RiskQ functions yielding, for example, corresponding moments, evaluations, inverse evaluations, truncated distributions, averaged distributions, standardized distributions, and simulated variates. Simulations are based by default on an efficient, constrained Latin-Hypercube approach to Monte-Carlo sampling that supports the generation of variates with a user-specified rank-correlation matrix. This default mode may be overridden to employ either a standard Latin-Hypercube or a random, uniform sampling strategy. As with all simulations of this nature, users are encouraged to repeat Monte-Carlo simulations using multiple, increasing sample sizes to verify the accuracy of the results obtained.

Additional RiskQ functions facilitate the characterization of uncertainty and discrete probability calculus. RiskQ also contains a variety of parametric and nonparametric statistical functions generating, for example, statistical analysis for means comparisons, distributional comparisons (Kolmogorov-Smirnov type tests), Gaussian fitting (of censored or uncensored data), (multiple) linear regression, correlation analysis, ANOVA/MANOVA, and homogeneity of one-way or multiway classified data.

RiskQ focuses on the cumulative probability distribution function (cdf) as a unifying theme in probability and uncertainty analysis. A special case of the cdf pertaining to discretely distributed variates is the cumulative probability mass function (cmf). RiskQ provides for the convenient transformation of any user-supplied (or empirical) data list, that is, vector or array of numerical values, into a corresponding empirical cmf or approximating empirical cdf. Of course, cdfs and cmfs for a variety of widely used statistical distributions may also be obtained directly, and these may be used in combination with empirical distributions for analysis within RiskQ. Probability mass functions (pmfs), may also be obtained within RiskQ. Probability density functions (pdfs) may not be obtained because the latter are only of use in describing a continuously distributed variate and cannot be used to describe a discontinuously distributed variate or a variate characterized as a mixture of continuously and discontinuously distributed values. Thus, RiskQ is designed to operate on variates with arbitrary distributional characteristics, provided they correspond to mathematically valid cdfs.