# Nonparametric, 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. »   Create Distributions Directly from Data » Use Nonparametric Distributions Like Any Other Distribution » Compute Any of Over 30 Nonparametric Distributional Properties »   Employ Nonparametric Data Models in Any Number of Dimensions » Estimate Multivariate Nonparametric Probabilities and Expectations » Analyze Left-, Right-, and Interval-Censored Data »   Use Nonparametric Distributions to Simulate Natural Processes » Create Confidence Envelopes about Nonparametric Density Estimates » Solve Optimization Problems in Density Estimation »   Create New Distributions from Existing Ones using Derived Distributions » Truncate a Distribution » Perform Affine Transformations on a Normal Distribution »   Apply Censoring to a Distribution » Create Joint Order Distributions » Visualize a Marginal Distribution »   Prepare a Table of Special Transformations » Generate a Gallery of Mixture Distributions » Use Different Copula Kernels »   Graph of Special Parameter Mixtures » Simulate a Derived Distribution » Visualize Iso-Probability Density Levels for a Product Distribution »   Compare Nonparametric and Parametric Reliability Models » Employ Nonparametric Distributions in Sophisticated Mixture Models » Create a Hierarchical Parameter Mixture Model »   Study the Properties of a Custom Probability Distribution » Model Claim Payments for Insurance » Create Your Own Distribution »