<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> / Thesis / Master of Science (MSc)
| Identifer | oai:union.ndltd.org:mcmaster.ca/oai:macsphere.mcmaster.ca:11375/17562 |
| Date | 04 1900 |
| Creators | Davis, Charles Shaw |
| Contributors | Stephens, M. A., Mathematics and Statistics |
| Source Sets | McMaster University |
| Language | English |
| Detected Language | English |
| Type | Thesis |
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