The Sampling Distribution of Some Goodness of Fit Test Statistics Using Burr Distribution And Censored Samples | ||||
| The Egyptian Statistical Journal | ||||
| Article 1, Volume 38, Issue 2, December 1994, Page 147-164 | ||||
| Document Type: Original Article | ||||
| DOI: 10.21608/esju.1994.314822 | ||||
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| Authors | ||||
| Samir K. Ashour; Abd-Allah M. Abd-Elfattah | ||||
| Abstract | ||||
| The Burr type XII distribution yields a wide range of values of skewness and kortosis and it can be used to fit almost any given set of unimodel data, so special attention has been focused on it. It has become an important family of distributions for Reliability studies. It is often of interest to determine whether a set of data can be considered to have come from a population belonging to this family. Three of the best known tests for goodness of fit are the Kolmogorov-Smirnov test (KS), the Cramer-Von Mises test (CVM) and the Anderson-Darling test (AD). These tests become extremely conservative when they are used in cases when the hypothesized distribution contains unknown parameters which must be estimated from the sample data. In this paper, we shall derive, numerically, the sampling distributions for the three test statistics, (KS, CVM and AD) in the case of censored samples, if the underlying distribution is Burr type XII with two unknown parameters. We have used the Pearson system, the Least Squares and a Software Package called STATGRAPHICS to derive their distributions. These distributions may be utilized to obtain critical values for each test statistics, to be used with small, medium and large sample sizes. | ||||
| Keywords | ||||
| Burr Distribution; Censored Samples; Goodness of Fit Test Statistics; Sampling Distribution | ||||
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Statistics Article View: 23 |
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