A new Birbaum-Saunders like distribution familiy

Lifetime distributions are statistical models that describe the time until an event of interest occurs and are frequently used in the applications of reliability, survival and risk analysis. One of these distributions, the Birnbaum-Saunders distribution, was introduced to model the lifetime of aircraft materials that are constantly exposed to vibration, and over time, its application area has increased and become one of the popular life distributions as a results of its properties. To further expand the application areas of this distribution and increase its flexibility, the generalized Birnbaum-Saunders family of distributions has been defined. Thus, new life distributions that have important features of the Birnbaum-Saunders distribution and are more suitable for asymmetric data have been produced. In this thesis, a new subfamily of the generalized Birnbaum-Saunders family is introduced. In this thesis, a new subfamily of the generalized Birnbaum-Saunders family is introduced. In the study, after examining the general characteristics of the family and the new distributions produced, a new distribution called the triangular Birnbaum-Saunders distribution, was examined in detail. So, the shape analysis of the distribution was made for density and hazard functions, their moments were given and order statistics were examined. Afterwards, seven different estimators were proposed to estimate the two parameters of the distribution and a detailed simulation study was given to examine the performances of the estimators. Finally, a real data analysis application were carried out to demonstrate the usefulness of the distribution and its advantages over other distributions currently used in the literature.