On discrete analogues of generalized lindley distributions and bivariate extension / Presented by Manal Mahmoud Ezzat Abdul Moneam Salem ; supervised by Prof. Moshira A. Ismail.

Thesis (Ph.D)-Cairo University, 2023.

Bibliography: pages 111-118.

Discrete distributions are needed and their importance increases day by day. Nonetheless it is also well known that the classical discrete distributions such as the geometric and Poisson are unsuitable for some situations because of their monotonic hazard rate functions. One way to overcome this problem is to discretize continuous distributions to get discrete distributions suitable to fit various types of lifetime data and to accommodate nonmonotonic hazard rate functions.

One objective of this study is to focus on the importance of providing an analytical study for the hazard rate function. The second one is to suggest two new discrete distributions by taking into account the discrete analogues of the two parameter weighted Lindley distribution and new generalized two parameter Lindley distribution. In addition, several properties of the newly proposed distributions are developed and the mixture representation of the probability mass function is derived. We explore the hazard rate shapes in details both theoretically and through plots. It is found that the two new suggested distributions have a hazard rate function that can take a bathtub shape, as well as other shapes.

Univariate distributions cannot capture two dimensional characteristics. Therefore, the third objective of this study is to construct two new different bivariate extensions based on the minimization approach by choosing the proposed discrete new generalized two parameter Lindley distribution as the baseline distribution. Several properties for the new distributions are studied.

For both univariate and bivariate distributions, the method of maximum likelihood estimation is used to estimate the unknown parameters. A detailed simulation study under several sets of parameters is conducted for each distribution. Finally, the applicability of the univariate distributions is illustrated using four real data sets whereas the flexibility of the bivariate distributions is investigated by analyzing two real data sets.

تعتبر نماذج الصدمات ونماذج المخاطر المتنافسة المقنعة أمثلة لتطبيق التوزيعين الثنائيين المقترحين. في هذه الرسالة سيتم استخدام توزيع لندلي المعمم الجديد المتقطع ذو معلمتين لتقديم توزيعيين ثنائيين مختلفين لتمثيل خصائص ثنائية الأبعاد. يتم الحصول على التوزيع الأول من خلال تغيير معلمة المقياس في التوزيعات الأساسية. في حين أنه يتم الحصول على التوزيع المقترح الثاني من خلال تغيير معلمة الشكل

Issues also as CD.

Text in English and abstract in Arabic & English.