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A General Outlook of DistributionProbe™

One common application of probability distributions is modeling univariate data with a specific probability distribution. This involves the following two steps:  

1. Determination of the "best-fitting" distribution.

2. Estimation of distribution related parameters (shape, location, and scale parameters).

DistributionProbe uses the goodness-of-fit technologies to determine the best-fitting distribution among fifteen distributions for the observed data while the distribution parameters were computed by the Method of Moments (MOM) and Maximum Likelihood Estimate (MLE). The goodness-of-fit technologies examine how well a sample of data agrees with a given distribution as its population. In this version of DistributionProbe uses the following three technologies for goodness-of-fit test:  

• Kolmogorov-Smirnov (K-S) test,

• Anderson-Darling test , and

• Cramer-von Mises test

 By selecting one of these test methods, the rank of the best fitted distributions is computed based on the significance levels of the observed data. The significance level measure the discrepancy between the empirical distribution function (EDF), a step cumulative density function calculated from the sample, and a given distribution function. The parameters of the given distribution are fully unknown and can be estimated by  Method of moments  (MOM) and Maximum likelihood (MLE) from sample.

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Last Updated 12/18/06

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