Thesis (M.Sc.) - Cairo University - Faculty of Graduate Studies for Statistical Research - Department of Mathematical Statistics

Nowadays, there is still a need for statistical models capable ofextracting all the information from the data, in order to communicate on them and make them useful as well. This is particularly the case in engineering, economics, biological studies and environmental sciences. For this reasons, several generations of statisticians have concentrated their efforts in improving the desirable properties of the probability distributions at the basis of these models, through various kinds of extensions or generalizations. In this thesis, a new four -parameter lifetime distribution, called the inverse Weibull Weibull distribution, is presented based on inverse Weibull-G family. Some mathematical properties of the stated distribution are discussed, including; quantile measures, moments, order statistics, incomplete moments, residual life function and entropy measure.The estimation of the model parameters is performed by maximum likelihood, least squares and Cramer-von Mises methods. Applications to real data sets are given to show the flexibility and potentiality of the proposed distribution. Furthermore, estimation of theinverse WeibullWeibull model parameters is discussed using maximum likelihood method based on progressive type II censored samples.Also, the maximum likelihood estimator of survival function and hazard rate function are derived. Furthermore, the approximate confidence intervals of model parameters, reliability and hazard rate functions are constructed. A numerical study is presented to check the performance of the estimates

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