Analysis of lifetime data using a new generator to build some families of probability distributions / Waleed Gouda Marzouk Morsi Hassan ; Supervised Abdelhadi N. Ahmed , Ali A. A-Rahman

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

Probability distributions are very important and fundamental to the real world and it is the basis for the study of uncertainty.The quality of the procedures used in a statistical analysis depends heavily on the generated distribution. In several applied fields such as medicine, engineering, and finance, among others, modeling and analyzing lifetime data are crucial. In the last few decades, the extended distributions have attracted the attention of many authors because the computational and analytical facilities available in programming software such as R, Maple, and Mathematica can easily tackle the problems involved in computing special functions in these extended distributions. This thesis focuses on developing new generating families of continuous univariate distributions to extend any continuous distribution. Therefore, three new families of distributions called the generalized odd Lomax generated family, the generalized odd linear exponential family and the generalized linear failure rate family are introduced in this dissertation. The most important features of these new families are the generation of distributions that have constant, decreasing, increasing, upside-down bathtub and bathtub shaped failure rate function depending on its parameters, also, it includes some well-known lifetime distributions as special sub-models. The new families also extend some well-known families in the literature. For the new families statistical and reliability properties are fully investigated. Several special distributions in the literature are derived from our newly introduced families as special cases. The importance and usefulness of the introduced families are demonstrated in applications by conducting simulation models and fitting real-world data

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