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

In many statistical situations, classical distributions do not provide appropriate {uFB01}ts to real data. Recently, attempts have been made to define new families of probability distributions that extendwell-known distributions and at the same time provide great flexibility in modelingdata in practice.In this thesis, a new four-parameter lifetime distribution, called the generalized transmuted moment exponential distribution is introduced.This distribution is a particular case from generalized transmuted-G family. Its density function is very flexible and can be symmetrical, unimodal and right skewed. Also, the hazard rate function of this distribution can be increasing and decreasing according to different values of parameters.Different stracture properties are showed including explicit expressions for the quantile function. Also, moments and incomplete moments, moments of the residual and reversed residual life and Rényi entropy are obtained.Additionally, the maximum likelihood, percentiles and least squares methods are used to estimate the modelparameters.The potentiality of the new model is illustrated by means of threeapplications to real data.The lower generalized order statistics is a unified model which contains the well-known decreasingly ordered random variables like lower order statistics, L-moments, TL-momets and lower record values.Simple expressions for single and product moments of lower generalized order statistics from generalized transmuted moment exponential distribution are provided. Somecomputional results of the means and variances of lower order statistics are carried out based on theortical results of lower order statistics for some sample sizes in a simple and efficient manner.Special moments like L-moments and TL- moments are also provided. Furthermore, characterization of the generalized transmuted moment exponential using the conditional moments is discussed

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