On the theory and practice of fitting distributions to data /
This research discusses some new ways of thinking about the
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| Format: | Thesis Book |
| Language: | English |
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[Place of publication not identified] :
[publisher not identified] ;
1997.
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| Online Access: | http://proxy.library.tamu.edu/login?url=http://proquest.umi.com/pqdweb?did=736824241&sid=1&Fmt=2&clientId=2945&RQT=309&VName=PQD |
| Summary: | This research discusses some new ways of thinking about the Anderson-Darling goodness-of-fit test and evaluates commercial data fitting software packages which determine distributions to represent sample data. Several new Anderson-Darling type tests are introduced and compared to the existing Anderson-Darling and Shapiro-Wilk tests for normality and exponentiality. Formulas are given for a new modified Anderson-Darling as a weighted "cumulative chi- square" statistics. New weight functions which emphasize the fit in the lower and upper quartiles of the sample are evaluated. Critical values are tabulated for all the new Anderson-Darling tests via Monte Carlo simulation for sample sizes of 12(4)60(20)300(100)1000, 1500, 2000, 3000, along with statistics AL2 and AU2 that emphasize lower and upper tails. These critical values are then used for a power study, using 40,000 repetitions of many alternate distributions, to test a composite hypothesis of normality with unknown mean and variance, and a composite hypothesis of exponentiality with unknown location and scale. For most sample sizes, the new statistics are shown to outperform the standard test statistics. Examples are given that show data fitting software packages are not incorporating the new technology offered by the extensive goodness-of-fit literature. |
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| Item Description: | Vita. "Major Subject: Statistics". |
| Physical Description: | xii, 127 leaves : illustrations ; 28 cm. Issued also on microfiche from University Microfilms Inc. |
| Bibliography: | Includes bibliographical references: pages 86-93. |