الفهرس 
Introduction and SummaryOnly 14 pages are availabe for public view
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Abstract
In practice, probability distributions are applied in such diverse
fields as actuarial science and insurance, risk analysis, investment, market
research, business and economic research, customer support, mining,
reliability engineering, chemical engineering, hydrology, image
processing, physics, medicine, sociology, demography etc.
Generally speaking, any probability distribution defined on the
positive real line can be considered as a lifetime distribution. Life time
refers to human life length, the life span of a device before it fails, the
survival time of a patient with serious disease from the date of diagnosis
or major treatment or the duration of a social event such as marriage.
Statistical analysis of lifetime data is an important topic in
biomedical science, social sciences, reliability engineering, among others.
Moreover, the quality of statistical analysis depends certainly on the
probability distribution used in this analysis. On the other hand, modeling
and analyzing lifetime data are crucial in various applied sciences.
However, the statistical literature contains many generalized
distributions, there still remain many important problems involving real
data, that do not follow any of the well-known models. So, many authors
have proposed several extensions of the well-known models to improve
model flexibility.
There are many techniques to construct new lifetime distributions.
For example, transformations of variables, transformations of distribution
reliability function, competing risk approach, linear combination of two hazard rate functions, probability integral transforms and compound
distributions, among others. For more details about these methods see Lai
(2013).
Our aim in this thesis is to define and study new three extensions
for the power Lindley, Lomax and Fréchet distributions using the
compound distributions and new generators techniques.
We have studied these three models and provide some of their
properties and the estimation of their unknown parameters was also
discussed using different three methods. The importance and flexibility of
these new distributions are examined empirically using real life data sets.
We show that the new models can give better fits than other competitive
models.
1.2 selecting the Best Distribution
Distribution fitting is the procedure of selecting a statistical
distribution that best fits to a data set generated by some random process.
In other words, if you have some random data available, and would like
to know what particular distribution can be used to describe your data,
then distribution fitting is what you are looking for.
Probability distributions can be viewed as a tool for dealing with
uncertainty: you use distributions to perform specific calculations and
apply the results to make well-grounded business decisions. However, if
one uses a wrong tool, one gets wrong results. If an inappropriate
distribution (the one that does not fit to your data well) is selected and
applied, the subsequent calculations will be incorrect, and that hence will
result in wrong decisions.