Genelleştirilmiş Olasılık Dağılımları Üzerine Bir Çalışma

Abstract

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.