الفهرس 
Background and MotivationOnly 14 pages are availabe for public view
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Abstract
The amount of data available for analysis is growing increasingly faster, requiring new probabilistic distributions to better describe each phenomenon or experiment studied. Computer based tools allow the use of more complex distributions with a larger number of parameters to better study sizeable masses of data. Many generalized (generated) families of continuous distributions have been developed and applied to describe various phenomena. These families of distribution have one or more shape parameters which allow a distribution to take on a variety of shapes, depending on the value of the shape parameter(s). This parameter(s) induction has also proved to be helpful in improving the goodness-of-fit of the new family of distributions. These distributions are particularly useful in modeling applications since they are flexible enough to model a variety of data sets and it have the ability to fit skewed data better than existing distributions. The literature in the field presents several methods for generating families of continuous distributions. The significance of these methods is that, depending on the situation, each method can generate a probability distribution that provides better fit to a data set. Most of these methods are addressed in this thesis. The thesis consists of six chapters, and it is structured as follows: The main objective of Chapter 1 is to make the thesis as much as possible a self-contained piece of research. It includes most of the main definitions, concepts, and theoretical results. Chapter 2 presents a comprehensive study concerned with most methods used for generating new families of continuous distributions. This chapter starts with the monumental work by Pearson (1890-1895) who presented asystematic approach for generating statistical distributions using differential equation. The main interest of this chapter is in families of distributions on the positive domain with additional shape parameter(s). The mathematical relationship between mixture cure rate model and promotion time cure rate model is considered, in Chapter 3, to generate a new three-parameter distribution called modified Gompertz (MG) distribution. Various statistical and reliability properties are investigated. The model’s parameters are estimated using maximum likelihood method. A simulation study is performed to examine the accuracy of the MLEs. Application to real dataset is used to examine the MG distribution compared to other extensions of Gompertz and some well-known models. Chapter 4 is devoted to propose a new family of distributions, called exponential power power series (EPPS) family of distributions. The hazard function of the new class can be increasing (I), decreasing (D), IDI and bathtub shaped. The moments and some characteristics for the probability density function of EPPS family are obtained. The maximum likelihood estimators (MLEs) of the parameters are discussed. A simulation study is performed to examine the accuracy of the MLEs. Applications to real datasets are given to show the desirable flexibility of the new family. Defective versions of modified Gompertz distribution and exponential power geometric (EPG) distribution (a member of EPPS family) are proposed in Chapter 5. More importantly, owing to the proposed defective distributions, cure rate regression models are proposed to model survival data contains immune individuals with associated covariates. The maximum ii likelihood method and Bayesian method are used for estimating the models’ parameters. A designated simulation algorithm is conducted to examine the performance of the used estimation methods. The superiority of the proposed models is illustrated via application a real dataset related to the survival times for group of patients diagnosed with tripe-negative breast cancer and how the cure rates affected by the primary tumor site and regional lymph node involvement. The DMG cure rate regression model is used to analyze a dataset related to the survival times of triple-negative breast cancer patients. The GEPG cure rate regression model is used to analyze a dataset related to the survival times of colon cancer patients. Chapter 6 concerned with a distribution defined on the unite interval, called unit-omega distribution. The unit-omega distribution is a special case of omega distribution which is generated based on omega function. Some probabilistic properties of the unit-omega distribution are derived and studied. Various estimation methods are used to estimate the distribution parameters. The performance of these estimation methods is examined and compared by conducting a simulation study. The quantile function of unit-omega distribution has a closed-form expression that allows modeling of quantiles in presence of covariates. The superiority of the proposed model is explored via applications to real data, one of them relates to child mortality rates and how these rates affected by proportion of people left behind across three key indicators: nutrition, availability of safe drinking source and adequate education.