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http://hdl.handle.net/11375/17562
Title: | Approximating Probability Distributions Using Moments |
Authors: | Davis, Charles Shaw |
Advisor: | Stephens, M. A. |
Department: | Mathematics and Statistics |
Keywords: | approximate significance points of random variables, random variables, approximatae significance, distributions, Pearson curves, Cornish-Fisher, a+bW, chi-squared, degrees of freedom, methods of approximation |
Publication Date: | Apr-1977 |
Abstract: | <p> We study the problem of finding approximate significance points of random variables whose exact distributions are unknown or extremely complicated . We consider the case where at least the first three moments, and possibly the lower or upper endpoint of the distribution are known. </p> <p> The methods of approximation studied include the Johnson system of transformations, Pearson curves, Pearson curves with known lower terminal, Cornish-Fisher expansions and the approximation a+bW, where W is chi-squared with p degrees of freedom . A new three-moment approximation of the form (cW)^k, with W as defined above, is also considered. These methods of approximation are discussed, with special attention to fitting procedures and computer implementation. </p> <p> The methods of approximation are compared, with respect to ease of application and accuracy of approximation, over a wide variety of exact distributions. The accuracy of each approximation is discussed and guidelines are given for determining which of several approximations should be used in a particular case. </p> |
URI: | http://hdl.handle.net/11375/17562 |
Appears in Collections: | Open Access Dissertations and Theses |
Files in This Item:
File | Description | Size | Format | |
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Davis_Charles_S_1977Apr_M.Sc..pdf | 33.75 MB | Adobe PDF | View/Open |
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