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

In various fields of science such as biology, engineering and medicine it is not possible to continuously observe or inspect the testing process and obtain the measurements of a statistical experiment exactly, but it is possible to classify them into intervals or disjoint subsets. So at this time, only grouped data will be suitable to be used.This thesis focuses on estimating the unknown parameters of exponentiated Fréchet and exponentiated inverted Weibull distributions based on grouped data with equi and unequi-spaced grouping. Comparison study between estimators made with respect to their biases and mean square errors using extensive simulation techniques. In addition the asymptotic optimal group limits and asymptotic relative efficiencies for maximum likelihood estimators of the unknown parameters with equi- and unequi-spaced grouping for both distributions are obtained. Furthermore, the estimation problem for the unknown parameters for exponentiated inverted Weibull distribution based on grouped and censored sample is considered. An iterative procedure is used to obtain the maximum likelihood and asymptotic confidence interval estimates numerically. To explain how the exponentiated inverted Weibull fits a set of real data better than other distributions an illustrative example is presented.

Issued also as CD