Core Algorithms
Nonparametrics, Derived, and Formula Distributions

Mathematica 8 introduces fundamentally new ideas in distributional modeling. The first is that of a nonparametric distribution that automates and generalizes a whole range of nonparametric methods used for computing specific distribution properties. The second is that of a derived distribution that is created from any existing distribution through common operations such as functional transformation, truncation, or mixing, etc. The third is that of a distribution defined by a formula such as a PDF, CDF, or survival function. The different types of distributions work together seamlessly, creating a modeling and analysis framework with unprecedented flexibility and ease of use.

Nonparametric distributions including empirical, histogram, smooth kernel, etc. »

Kernel density estimation with automatic fixed or adaptive bandwidth selection. »

Optimized univariate and multivariate empirical distributions. »

Nonparametric maximum-likelihood estimation for censored data. »

Efficient survival and reliability modeling with truncated and censored distributions. »

Derived distributions including transformed, truncated, mixtures, etc. »

Univariate and multivariate transformations of random variables. »

Univariate and joint distributions of order statistics from any distribution. »

Component mixture distributions with arbitrary component distributions. »

Parameter mixture distributions with discrete and continuous weight distributions. »

Truncated distribution of any dimension, continuous and discrete. »

Censored distribution of any dimension, continuous and discrete. »

Copula distributions for multiple kernel families and any marginal distributions. »

Marginal distributions of any dimension from any higher-dimensional distribution. »

Distributions defined from formulas of PDF, CDF, or survival functions. »

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