Genelleştirilmiş Olasılık Dağılımları Üzerine Bir Çalışma
Özet
Numerous classical distributions are used in the modeling of acquired data in engineering,
actuarial, environmental and medical sciences, demography, economics, finance, insurance,
biological studies, life analysis and many other fields. However, it can be seen that in some
areas such as life analysis, finance, insurance, these distributions may be insufficient in the
data modeling. This problem has led to the need for distributions to be more flexible in data
modeling. This requirement has increased the studies done on defining new probability
distribution families by extending the known distribution families.
In defining new distribution families, "generator distributions" are commonly used as well as
methods such as exponentialization, transformation, and parameter addition. Here, meaning of
the “generating” is to obtain a different F distribution for each different G distribution. The
distribution called the generator is the distribution giving the name to the generalized
distribution family.
In the thesis study, three new distributions are proposed, which will be an alternative in
modeling data sets (right-skewed, left-skewed, heavy-tailed, etc.). These new distributions are
Kumaraswamy Generalized Distribution Family, Marshall-Olkin Distribution Family and
Kumaraswamy Marshall-Olkin Distribution Family members. The generator distribution
approach and additional parameter methods have been taken into consideration in defining the
distributions. These distributions are called Kumaraswamy Lindley (KL), Marshall-Olkin
Rayleigh (MOR) and Kumaraswamy Marshall-Olkin Log Logistics (KMOLL) distributions.
Moreover, in the last part of the thesis, a new family of distributions, which contains many
distributions; The Lindley Generalized Distribution family was obtained. All properties of this
family are examined and the relationship with the existing distribution families is considered.
