Core Algorithms

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 »


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