Thesis (Ph.D.) - Cairo University - Institute of Statistical Studies and Research - Department of Mathematical Statistics

At the core of all statistical analyses, there exists a model that attempts to describe the underlying structure or relationship of some phenomena on which measurements are taken. Statistical tests, estimation procedures, and inference are based on these sampled measurements data) and a hypothesized model. Procedures used to verify and validate these model or distributional assumptions are known as goodness of fit tests. One popular approach for testing a goodness of fit is based on a discrepancy measure between the empirical distribution function and the hypothesized distribution function. Examples include the well known goodness of fit tests of a fully specified null hypothetical distribution to data are the kolmogorov smirnov (KS), cramer von mises (CvM) and anderson darling (AD) tests. recently, grane' (2012) proposed another approach for testing a completely specified goodness of fit test with type-II censoring schemes that based on hoeffding's maximum correlation. Also goldmann et al. (2015) suggested approach to test a goodness of fit with type-II censoring samples based on data transformations. In this study, we restrict our attention to modify these tests for flexible weibull and inverse flexible Weibull distributions. The maximum likelihood method of estimation is used for estimating the parameters. Critical values are obtained for the modified KS, CvM and AD test statistics in case of complete and type-II censored samples, a goodness of fit test based on data transformations and a goodness of fit test based on Hoeffding's maximum correlation with type-II censoring schemes through monte Carlo simulation

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