الفهرس 
LINDLEY DISTRIBUTION AND ITS APPLICATIONOnly 14 pages are availabe for public view
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Abstract
The modeling and analysis of lifetime is an important aspect of statistical
work in a wide variety of scientific and technological fields. The failure
behavior of any system can be considered as a random variable due to the
variations from one system to another resulting from the nature of the
system. Therefore, it seems logical to find a statistical model for the failure
of the system. In other applications, survival data are categorized by their
hazard rate, For example, there are distributions with fixed hazard rate such
as the exponential distribution. Other distributions are characterized by
incremental hazard rate. Some have decreasing failure rate, and others
combine the three kinds on different time periods to appear in the the form of
bathtub.
The Kumaraswamy distribution is similar in its simplest form to the beta
distribution in terms of probability density function and cumulative
distribution function. This distribution has an advantage to the beta
distribution, because it is simpler to use especially in simulation studies.
The Kumaraswamy distribution is applicable to many natural phenomena ,
such as the heights of individuals, scores obtained on a test, atmospheric
temperatures, hydrological data and landslides. It can be a useful tool to
analyze customer lifetime duration in marketing research and can be used
quite effectively in analyzing real data. This distribution is in use in
electrical, civil, mechanical, and financial engineering applications.
The Kumaraswamy distribution arises depending on order statistics, and its
form clearly does not depend on special functions, thus have a distinct role in
ease of statistical modeling, it also has a tendency for application in
educational uses.
In recent years, generalized distributions have been widely studied in
statistics as they possess flexibility in applications. This is justified because
the traditional distributions often do not provide good fit in relation to real
data set studied.
In this thesis, according to Kumaraswamy distribution we propose a new
class of generalized distributions called the Exponentialed Kumaraswmay
Lindley (EKumL) that is capable of modeling bathtub-shaped hazard
function. The beauty and importance of this distribution lies in its ability to
model monotone and non-monotone failure rate function, which are quite
common in lifetime data analysis and reliability.
The thesis consists of three chapters as follows:
Chapter I: contains the concepts and basic characteristics of the Lindley
distribution and its applications. Some of the previous research on the
different forms of the Lindley distribution are presented.
Chapter II: we introduce Kumaraswamy distribution and we present some
statistical properties such as the mode, quantile function and moments. In
addition, estimation of the parameters using the maximum likelihood method
and display elements of the information matrix. We present many of
distributions using generalization Kumaraswamy distribution and the
analytical shapes of the corresponding probability density functions are
derived with graphical illustration. Applications using real data sets are
given.
Chapter III: constitutes our main goal, which is a complete review of the
Exponential Kumaraswamy Lindley distribution. Some basic properties of
this distribution, such as quantil function, moments, moment generating
function and entropy are derived. as well as the derivation of maximum
likelihood estimates of the parameters and the observed and expected
information matrix. Finally, numerical examples are given using sets of real
data, A simulation study is conducted to demonstrate the effect of the sample
on the estimates of the parameters and its characteristics. The results of this
chapter are published in ”Journal of Statistics: Advances in Theory and
Applications”. 2015, 14(1), 69-105.