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

Indeed, mixture models have been widely used in many domains, including econometric, psychosocial, genetic, medical researches, astronomy, engineering, and marketing, among many other fields. A mixture distribution is a compounding of statistical distributions, which arise when sampling from nonhomogeneous populations (or mixed) with different probability density function in each component. For example; the distribution of some diagnostic measures in a mixed population of patients some of whom have a given disease and some of whom do not. The xgamma distribution is a new mixture model from exponential and gamma distributions. In many situations, it is often impossible to obtain the measurements of a statistical experiment exactly, but it is possible to classify them into intervals, or disjoint subsets. The resulting data are known as grouped data (e.g. the personal income data reported by government originations). The objective in the present thesis is to study the parameter estimation of the xgamma distribution via grouped data due to it is importance. Maximum likelihood, minimum chi-square, modified minimum chi-square, least squares and least lines estimators are derived in equi and unequi-spaced grouping. Numerical study is carried out to compare the performance of different estimators in each case. Moreover, the maximum likelihood estimators are derived based on grouped and censored data in equi- and unequi-spaced grouping. Numerical study is employed to evaluate the performance of estimates

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