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On the Computation and Power of Goodness-Of-Fit Tests

On the Computation and Power of Goodness-Of-Fit Tests


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About the Book

This dissertation, "On the Computation and Power of Goodness-of-fit Tests" by Jingbo, Wang, 王靜波, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Abstract of thesis entitled "On the Computation and Power of Goodness-of-fit Tests" Submitted by Jingbo WANG for the degree of Master of Philosophy at The University of Hong Kong in September 2005 This thesis studies the computation and power of the two most common goodness-of-fit tests for continuous samples, the Kolmogorov-Smirnov test and the Anderson-Darling test. Several previous studies have been conducted to evaluate the distributions of the Kolmogorov statistic and the Anderson-Darling statistic in the known parameter case, where all the parameters of the hypothetical distribution are specified before applying the test. However, in practice, the parameters are oftenestimatedfromthesamesamplesfortesting(theunknownparametercase). The distributions of the two statistics in the unknown parameter case are more difficult to evaluate. So far no practical method has yet been developed. Some users just use the distribution in the known parameter case in applying a test with unknown parameters. This could cause serious errors in computation. We developed an approximation method for evaluating the distributions of the two statistics in the unknown parameter cases of normality testing and ex- ponentiality testing. The method exploits a relation between the statistic with known parameters and that with unknown parameters. The relation enables us to compute the distribution of the latter from that of the former. The method is fastandaccurate, andcoversawiderangeofn(sizeofsamplesbeingtested). Be- sides, in the known parameter case, we implemented the long forgotten method suggestedbyDurbin, whilealsodevelopinganewalgorithmtoevaluatethedistri-butionoftheKolmogorov statistic. WealsoimprovedMarsaglia's approximation formula of the distribution of the Anderson-Darling statistic by multiplying an amendatory factor to it. We compared the power of the two tests together with the chi-square test using various alternative distributions. It was found that the Anderson-Darling test was the stronger in most cases. The outcome of this study is beneficial to both statisticians and more im- portantly, users of goodness-of-fit tests. ----------------- Total words for the abstract: 299 words DOI: 10.5353/th_b3199865 Subjects: Sampling (Statistics) Goodness-of-fit tests Nonparametric statistics


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Product Details
  • ISBN-13: 9781361234150
  • Publisher: Open Dissertation Press
  • Publisher Imprint: Open Dissertation Press
  • Height: 279 mm
  • No of Pages: 88
  • Weight: 499 gr
  • ISBN-10: 1361234156
  • Publisher Date: 26 Jan 2017
  • Binding: Hardback
  • Language: English
  • Spine Width: 6 mm
  • Width: 216 mm


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