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العنوان
Estimation of Stress-Strengths Reliability for Some General Bivariate Distributions /
المؤلف
Abd El-Razik, Diana Ahmed Mohamed.
هيئة الاعداد
باحث / دينا احمد محمد عبد الرازق
مشرف / ناهد عبد السلام مخلص
مشرف / سهير خميس خميس جمعة
تاريخ النشر
2021.
عدد الصفحات
176 p. :
اللغة
الإنجليزية
الدرجة
ماجستير
التخصص
الإحصاء والاحتمالات
تاريخ الإجازة
1/1/2021
مكان الإجازة
جامعة عين شمس - كلية العلوم - الرياضيات
الفهرس
Only 14 pages are availabe for public view

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Abstract

The main objective of this thesis is the point estimation of a stress-strength model, R=(X_1>X_2), in two cases: the first case when X₁ and X₂ are dependent variables with marginal distribution functions having the same forms of distribution general exponential or general inverse exponential forms. The second case is when X₁ and X₂ are dependent variables with marginal distribution functions having different forms of distribution general exponential and general inverse exponential forms or vice versa. Different point estimators are obtained by different methods which can be classified into two main methods, the classical point estimation method and the Bayesian method. The estimation is performed based on complete sample and double Type II censored sample which contain the left Type II censored sample, right Type II censored sample and complete sample as special cases. Various statistical distributions in the literature possess the general exponential and the general inverse exponential forms. So, the results obtained can be applied to all these distribution. As illustration of the results obtained, Weibull and generalized inverted exponential are applied as example of general exponential form. While Burr III and generalized exponential are applied as example of general inverse exponential form. Simulation studies are also carried out for comparison of the different point estimators obtained. The comparison is based on mean squared error and the bias of the different estimators. A real life data set is also presented to demonstrate the applicability of the forms studied and the results obtain.