Agamy, M. (2021). A Comparative Study of Bayesian and Non-Bayesian Estimations for New Generalized Inverted Weibull Distribution. test, 27(1), 72-96. doi: 10.21608/jsfc.2021.293212
Mohamed Abdelsalam Agamy. "A Comparative Study of Bayesian and Non-Bayesian Estimations for New Generalized Inverted Weibull Distribution". test, 27, 1, 2021, 72-96. doi: 10.21608/jsfc.2021.293212
Agamy, M. (2021). 'A Comparative Study of Bayesian and Non-Bayesian Estimations for New Generalized Inverted Weibull Distribution', test, 27(1), pp. 72-96. doi: 10.21608/jsfc.2021.293212
Agamy, M. A Comparative Study of Bayesian and Non-Bayesian Estimations for New Generalized Inverted Weibull Distribution. test, 2021; 27(1): 72-96. doi: 10.21608/jsfc.2021.293212

A Comparative Study of Bayesian and Non-Bayesian Estimations for New Generalized Inverted Weibull Distribution

المجلة العلمية لقطاع کليات التجارة بجامعة الأزهر
Article 4, Volume 27, Issue 1, January 2022, Pages 72-96    PDF (884.67 K)
Document Type: المقالة الأصلية
DOI: 10.21608/jsfc.2021.293212
Author
Mohamed Abdelsalam Agamy*
Department of Statistics, Faculty of Commerce((Boys’ Branch) Alazhar University, Cairo
Abstract
This research proposes a new extension of the inverted Weibull distribution (IW) to provide a more adaptable distribution for modelling lifetime data, called the new inverted Weibull X-Gamma (NIWXG) distribution class.  Inverted Weibull, inverted Rayleigh, inverted exponential, X-Gamma inverted Rayleigh, and X-Gamma inverted exponential distributions are included as special sub-models in the suggested distribution. For certain values of the parameters, the probability density and hazard rate curves are sketched in all feasible configurations. Our main goal is to estimate its unknown parameters using non-Bayesian estimation techniques such as maximum likelihood estimation, Cramér-von-Mises estimation, least squares estimation, weighted least squares estimation, and Bayesian estimation under squared error loss function and LINEX loss function, as well as to derive some of its mathematical properties. We utilize extensive numerical simulations for both small and big samples to compare the performances of the non-Bayesian and Bayesian estimators. Based on the relative absolute bias and root mean squared error criterion, the results demonstrate that the Bayesian estimation is the best estimation.
الملخص
يقترح هذا البحث امتدادًا جديدًا لتوزيع معكوس وايبل (IW) لتقديم توزيع أكثر قابلية وتهيئة لنمذجة بيانات العمر، تسمى فئة توزيع معكوس ويبل اكس جاما (Weibull X-Gamma)  الجديدة (NIWXG).  تم تضمين كل من توزيع معكوس ويبل، وتوزيع معكوس رايلي، ومعكوس الأسي، ومعكوس اكس جاما (X-Gamma)، وتوزيعات معكوس X-Gamma الأسية  كنماذج فرعية خاصة في التوزيع المقترح. يتم رسم منحنيات دالة كثافة الاحتمال ومعدل الخطر لجميع التكوينات الممكنة. الهدف الرئيسي هو تقدير معلمات التوزيع المقترح غير المعروفة باستخدام تقنيات التقدير غير البايزية مثل تقدير الامكان الأكبر وتقدير كرامر - فون ميزس (Cramér-von-Mises) وطريقة تقدير المربعات الصغرى وطريقة المربعات الصغرى الموزونة وتقدير بايزي في ظل دالة خسارة الخطأ التربيعية ودالة خسارة لينكس  (LINEX)، وكذلك اشتقاق بعض خصائصه الرياضية. استخدم لتحقيق هذا الهدف عمليات محاكاة عددية مكثفة لكل من العينات الصغيرة والكبيرة لمقارنة أداء المقدر غير البايزي والمقدر البايزي. بناءً على معيار التحيز النسبي المطلق ومعيار جذر متوسط مربعات الخطأ، تظهر النتائج أن التقدير البايزي هو أفضل تقدير.
Keywords
Inverted Weibull distribution; Non-Bayesian estimation; Simulation study; Bayesian estimation; Root mean squared error; Quantile function توزيع معكوس وايبل; تقدير غير بايزي; دراسة محاكاة; تقدير بايزي; جذر متوسط مربعات الخطأ; الدالة الربيعية
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