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# Parameter Estimation and Testing

Leveraging Mathematica's seamless integration of symbolic and numeric capabilities, Mathematica 8 provides highly automated and efficient parameter estimation and goodness-of-fit testing for the more than 100 built-in parametric distributions and derived distribution constructors. Automatic selection of solvers and optimization routines allows the user to focus on the questions they want to answer instead of worrying about the algorithmic details, while optional settings allow the expert full control over the optimization and specific hypothesis tests if desired. Estimation and testing can be done in a few short lines of code, letting the researcher, analyst, educator, or student quickly move on to the decision-making and report-generation stages of their work.

• Highly automated parameter estimation for all parametric and derived distributions. »
• Maximum-likelihood and moment-based parameter estimates. »
• Goodness-of-fit testing for univariate, multivariate, discrete, and continuous data. »
• Automated location and scale hypothesis tests for any number of datasets. »
• Full suite of named location and scale tests, including , , sign, Levene, etc. »
• Complete set of test results, including test statistics, -values, reports, etc. »
 Fit Data to Any Type of Distribution » Directly Specify What Distribution and Parameters to Estimate » Estimate Parameters and Test Goodness-of-Fit » Visualize Optimal Parameter Values » Estimate using Likelihood or Moment-Based Methods » Model Word Lengths by Binomial Distributions » Use Component Mixtures to Model Multimodal Data » Decompose Mixture Models of Earthquake Magnitudes » Compare Two Models of Wind Speeds » Model City and Highway Gas Mileage with a Bivariate Normal Distribution » Test for Goodness-of-Fit to Any Distribution or Dataset » Perform Tests of Location and Scale for any Number of Datasets Simultaneously » Choose Parametric Tests or Their Nonparametric Counterparts » Explore Properties of Hypothesis Tests » Use General Hypothesis Test Functions to Automatically Select Tests » Compare Maximum-Likelihood and Cramér-von Mises Estimates » Use Hotelling's Test to Detect Counterfeit Bills » Compare Multivariate Sign Test Statistics with Spatial Signs of Data » Simulate, Visualize, and Compare Power Curves for Tests of Location » Visualize Distribution Functions for a Fitted Multivariate Distribution » Compare Distribution Functions for Estimated and Theoretical Copulas »

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