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Activity Number:
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58
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Type:
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Topic Contributed
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Date/Time:
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Sunday, August 2, 2009 : 4:00 PM to 5:50 PM
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Sponsor:
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Section on Statistics in Defense and National Security
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| Abstract - #303334 |
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Title:
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Fitting Univariate Probability Density Functions to Small Data Sets
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Author(s):
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Jerry L. Alderman*+ and William C. Thomas
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Companies:
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Raytheon Missile Systems and Raytheon Missile Systems
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Address:
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1151 E. Hermans Rd,, Tucson, AZ, 85756,
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Keywords:
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pdf fitting ; johnson distributions ; lambda distribution ; goodness-of-fit
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Abstract:
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This paper will illustrate the application of a genetic search algorithm for fitting Johnson Distributions to small data sets. Goodness of fit is assessed by computing the fraction of all possible subsets of a given data set that fall inside spec limits computed for the test statistic at specified confidence levels. This is similar to an application of U-Statistics and has the effect of leveraging the amount of info one can extract from a small data set. A statistic, RuM, is used for this purpose. An Excel-based tool that does the fitting includes a feature that generates all the subsets and computes the test statistic for each. For data sets of size n <= 30), Excel memory limitations restrict subset sizes to about 8, but tens to hundreds of thousands of independent statistical tests can be evaluated in this way in a few minutes.
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