Abstract
On the Methods of Generalization Known
Probability Distributions


The probability distribution is one of the most important topics
in the field of statistics and probabilities because of its
importance in the analysis and modeling of data in many
sciences. In recent years, the importance of the methods of
generalization, especially the new families, has increased as a
basis for deriving new probability distributions used to analyze
data in the fields of reliability, Business, meteorology, quality
control, statistical process monitoring and other fields to suit
these modern distributions of different types of data.

There is no doubt that the three distributions mentioned in this
thesis are of great importance in the study and analysis of the
reliability of data associated with distributions of life and this
led the researcher to use these families as a basis to derive new
distributions in the same field to bridge the gap in the analysis of
life data and despite the great efforts in the development and
conclusion of new distributions, but there are still many
important problems, which are Its data does not match any of
the existing distributions. The aim of this thesis is to present
three new probability distributions (OBBXII) distribution, (OLEW) distribution, (EGFrP)
distribution. Using three new families as a basis in their
conclusion (OB-G) family, (OL-G) family, (EGGP) Family.
The thesis included six chapters :
Chapter 1: Contains introduction and summary of the
objectives and Organization of the thesis.
Chapter 2: Contains basic definitions and scientific facts used
in the thesis.
Chapter 3: Introduces a new generalization for Burr XII with
most of its reliability and statistical characteristics with the
application where this distribution is called The Odd Burr Burr
XII distribution.
Chapter 4: Provides a new generalization of Exponentiated
Weibull distribution with the derivation of what is also related to
its reliability and statistical characteristics with the application
where this distribution is called The Odd Lindley Exponentiated
Weibull distribution.
Chapter 5 : Introduces a new generalization for the Fréchet
distribution with the derivation of what is also related to its
reliability and statistical characteristics with the application
where this distribution is called The Exponentiated Generalized
Fréchet Poisson distribution
Chapter 6 : Contains the findings of the research results and
proposed solutions for future research.