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

Several probability distributions have been proposed in the literature, especially with the aim of obtaining models that are more flexible to the behaviors of the density and hazard rate function. Recently, Barco et al. (2017) proposed the inverse power Lindley as the generalized form of inverse Lindley distribution. They showed that the inverse power Lindley distribution is a good alternative to some other models in modeling survival data. The main aim in the preset thesis is, firstly, to estimate the model parameters of inverse power Lindley based on four different methods of estimation. The proposed methods are the maximum likelihood, least squares, weighted least squares and percentiles. An intensive numerical study is conducted for evaluating the performance of parameter estimates. The comparison is mainly made between different estimates by using extensive simulation techniques.Secondly, the problem of optimal designing and statistical inference in step stress partial accelerated life test is considered under Type I censuring. The maximum likelihood is used to estimate the accelerated factor and the unknown parameter for the model. The asymptotic variance-covariance matrix and the confidence bounds of the parameters are also obtained. The optimum test plans for step stress partial accelerated life tests are developed. Such plans minimize the generalized asymptotic variance of the maximum likelihood estimators for the model parameters. Simulation study is used to illustrate the theoretical results

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