الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
The quality of procedures utilized in statistical analysis fundamentally relies upon the proposed lifetime distribution. Great efforts have been made in the development of large classes of standard lifetime distributions alongside pertinent statistical methodologies. The varying techniques of proposing generalized classes of standard lifetime distributions have attracted theoretical and applied statisticians because of their flexible properties. Most of the generalizations are developed for one or more of the following reasons: a physical or statistical theoretical argument to explain the mechanism of the generated data, a suitable model that has recently been utilized effectively, and a model whose empirical fit is good for the data. Therefore, the extension of the existing lifetime distributions is essential for applications. There are two basic types of topics to analyze any of the new generalized lifetime distributions, namely:
The statistical properties, like, moments, moment generating function, hazard rate function, reversed hazard rate function, mean residual lifetime, mean waiting time, variance residual lifetime, variance reversed residual lifetime, are very important for defining and describing the new lifetime distribution.
Statistical inference is a set of statistical methods used to study a population phenomenon based on a random sample of data. It divides into two main parts:
The first is the estimation (point and interval estimations) which is applied under the data collected from a complete sample (the time of the failure of life is recorded for each unit of the tested sample) or censored sample (it is difficult to record the time of the failure of all tested sample units).
The second is the testing hypothesis which is used to make a correct scientific decision about specific hypotheses for population parameters.
The main purpose of this thesis is to generate and develop new lifetime distributions, namely, generalized linear exponential, inverted generalized linear exponential, and modified generalized linear exponential distributions, using three different techniques. The statistical properties and the estimation of the unknown parameters under complete data are obtained for all proposed lifetime distributions. The constant partially accelerated life test with a progressive Type-II censoring scheme and the estimation of the unknown parameters using progressive first failure censoring scheme are also obtained for the inverted generalized linear exponential distribution.
The thesis consists of seven chapters
Chapter 1 contains some of the important definitions and some basic concepts which have been used throughout this thesis. A historical survey on some studies in statistical lifetime distributions, estimation, and accelerated lifetime test are also presented.
In Chapter 2, some basic definitions and some statistical properties for generalized linear exponential distribution, which were proposed by Mahmoud and Alam (2010), are given. The explicit forms of moment generating function and mean residual lifetime are calculated for this distribution. The maximum likelihood, the least square, the weighted least square, the Cram´er Von-Mises, and the Anderson-Darling estimations are derived from this distribution based on complete data. Two real data sets and numerical simulation are used for illustrative the theoretical results and for comparing the proposed different methods of estimations.
Chapter 3 introduces a new extension of the generalized linear exponential distribution, to be known as an inverted generalized linear exponential distribution. The sub-models of this new distribution are presented and the shapes of its probability density, hazard rate, and reversed hazard rate functions are investigated. Some statistical properties, like, moments, quantile, and modes for this distribution are studied. The explicit forms for mean residual lifetime, mean waiting time, variance of residual life, and variance of reversed residual life are calculated for this distribution and their behaviors are studied. Some measures of income inequality are also derived. The estimation of its unknown parameters by maximum likelihood is discussed. Four real data sets are used for comparing this distribution with some other well-known distributions based on Kolmogorov-Smirnov, Anderson-Darling, and Cram´er Von-Mises tests.
In Chapter 4, the problem of statistical estimation and optimal censoring using progressive first-failure censoring from inverted generalized linear exponential distribution are studied. The maximum likelihood estimation is presented to estimate the unknown parameters. An approximate confidence interval is constructed to compute the interval estimation for the parameters and the delta method is used to compute the interval estimation for survival, hazard rate, and reversed hazard rate functions. The Gibbs sampler with the Metropolis-Hastings algorithm is applied to generate the Markov chain Monte Carlo samples from the posterior functions to approximate the Bayes estimation using several loss functions and to establish the symmetric credible interval for the parameters. Two real data sets are used to study the suggested censoring schemes and the optimal censoring is used to show the performance of the censoring schemes using maximum likelihood estimator and Bayes estimator. Also, a new extension is studied to obtain the optimal censoring using Bayes estimator under varying loss functions. A simulation study is presented to compare the different estimation methods based on mean square error and average absolute bias.
Chapter5 concerns with the problem of the inference in constant partially accelerate life test from an inverted generalized linear exponential distribution based on progressive Type-II censoring scheme. The maximum likelihood estimation is presented to estimate the unknown parameters and the acceleration factor. The Gibbs sampler with the Metropolis-Hastings algorithm is applied to generate the Markov chain Monte Carlo samples from the posterior functions to approximate the Bayes estimation using several loss functions based on progressive Type-II censoring scheme. A real data set and a simulated data are analyzed for illustrative purposes. A simulation study is presented to compare the obtained estimates based on mean square error and average absolute bias.
In Chapter 6, a new modification of the generalized linear exponential distribution, to be known as a modified generalized linear exponential distribution, is introduced. The sub-models of this new distribution are presented and the shapes of its hazard rate function are investigated. Some of the mathematical properties of this distribution are studied including moments and moment generating function. The classification of the behavior of this distribution based on reliability analysis like mean residual lifetime and the variance residual lifetime are discussed. The estimation of its unknown parameters by the maximum likelihood estimation is derived under complete data. Two applications are used to show that the proposed distribution is a viable distribution in modeling lifetime data.
Chapter 7 studies the estimation of the unknown parameters for modified generalized linear exponential distribution by varying methods including, the maximum likelihood, the least square, the weighted least square, the Cram´er Von-Mises, and the Anderson-Darling estimations under complete data. Two applications are used to show that the proposed distribution is a viable distribution in modeling lifetime data. A simulation study is presented to compare the varying methods of estimation based on the mean square error and the average absolute bias.