An important problem in statistics is to obtain information about the form of the population from which the sample is drawn. Goodness of fit (GOF) tests is employed to determine how well the observed sample data “fits” some proposed model. The well known standard goodness of fit tests; Kolomogorov-Smirnov (KS), Cramer von Mises (CVM) and Anderson-(AD) tests are used for continuous distributions. When the parameters are unknown, the standard tables for these tests are not valid. The complete sample procedures of goodness of fit tests are inappropriate for use with censored samples. The critical values obtained from published tables of the complete sample test statistic are necessarily conservative.In this paper, we obtain the tables of critical values of modified Kolmogorov-Smirnov (KS) test, Cramer-Von Mises (CVM) test and Anderson-Darling (AD) test for the Compound Rayleigh (CR) distribution with unknown parameters in the case of complete and type II censored samples. Furthermore, we present power comparison between KS test, CVM test and AD test for a number of alternative distributions. Applications of the considered distribution to real medical data sets given by Stablein et al. (1981) are presented.
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机译:统计中的一个重要问题是获取有关从中抽取样本的总体形式的信息。拟合优度(GOF)测试用于确定观察到的样本数据“拟合”某些提议模型的程度。众所周知的拟合优度标准;连续分布使用Kolomogorov-Smirnov(KS),Cramer von Mises(CVM)和Anderson-(AD)测试。如果参数未知,则这些测试的标准表无效。拟合优度检验的完整样本程序不适用于受检样本。从完整样本检验统计量的已发布表格中获得的临界值一定是保守的。在本文中,我们获得了改进的Kolmogorov-Smirnov(KS)检验,Cramer-Von Mises(CVM)检验和Anderson-Darling检验的临界值表。 (AD)在完整和II类审查样本的情况下测试未知参数的复合瑞利(CR)分布。此外,我们提出了在KS测试,CVM测试和AD测试之间针对多种替代分布的功率比较。考虑的分布在Stablein等人给出的真实医学数据集上的应用。 (1981)提出。
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