Khater Abd El Hameed Gadelrab Kenaway,  <br/><br/>
Some characterizations based on  generalized order statistics / 
 بعض طرق التميز باستخدام الاحصاءات الترتيبية المعممة 
by Khater Abd El Hameed Gadelrab Kenaway ; Supervised Prof. Ali Ahmed Abdulrahman,,Prof. Ibrahim B. Abdul-Moniem, Prof. Salwa Mahmoud Samy Assar. 
 - 131 Leaves :   illustrations ;   30 cm. +   CD. 
<br/><br/>Thesis (Ph.D)-Cairo University, 2025. 
<br/><br/>Bibliography: pages 124-130. 
<br/><br/> The characterizations based on generalized order statistics are crucial for <br/>theoretical advancements and practical applications across various fields. Their <br/>ability to provide detailed insights into the distributional properties of ordered <br/>data makes them indispensable tools for statisticians, engineers, data scientists, <br/>and researchers. Characterizations based on generalized order statistics deepen <br/>our understanding of the structural properties of ordered data. By extending <br/>classical results, generalized order statistics offer new insights into the behavior <br/>and relationships of statistical distributions. <br/> This study explores some characterizations based on generalized order <br/>statistics from Weibull-Family of Life distributions, characterization based on <br/>recurrence relation for single moments of generalized order statistics, and <br/>characterization based on recurrence relation for product moments of <br/>generalized order statistics. <br/> The study investigates some characterizations based on generalized order <br/>statistics for many distributions, the recurrence relation for single expectations <br/>of generalized order statistics, and moments of order statistics.  Additionally, it <br/>tackles L-moments, TL-momets, and upper record values, characterization based <br/>on recurrence relation for single moments of generalized order statistics, and <br/>characterization based on recurrence relation for product moments of generalized <br/>order statistics. Some computational results of the means and variances of order <br/>statistics are carried out based on theoretical results of order statistics for some <br/>sample sizes simply and efficiently. Special moments like L-moments and TL- <br/>moments, as well as the characterization of generalized order statistics, are also <br/>provided.   تتناول هذه الدراسة توظيف الإحصاءات الترتيبية المعممة (Generalized Order Statistics - GOS)كأداة متقدمة لتحليل البيانات وتوصيف التوزيعات الاحتمالية، بما يسمح بفهم خصائصها خاصة في حالات البيانات غير التقليدية أو المقطوعة. انطلقت الفكرة من توسيع الإحصاءات الترتيبية التقليدية لتشمل تشكيلات أكثر تعقيدًا، مما وفر إطارًا مرنًا لدراسة المتغيرات العشوائية المرتبة وتطبيقاتها في مجالات الموثوقية وتحليل السلاسل الزمنية وإدارة المخاطر.<br/>تضمن العمل عرضًا لأهم الدراسات السابقة مثل أعمال Kamps (1995) وKeseling (1999) و Cramer and Kamps (2000) وAhsanullah (2000, 2016) وغيرهم، والذين تناولوا توصيف التوزيعات باستخدام GOS والقيم القياسية (Record Values). وقدّمت دراسات أخرى مثل Ahmed (2007) وKhan et al. (2007) وAL-Hussaini et al. (2005) إسهامات في تحليل العزوم وتوصيف التوزيعات الاحتمالية اعتمادًا على هذه الإحصاءات 
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<br/><br/><br/>Text in English and abstract in Arabic & English. 
<br/><br/><label>Subjects--Topical Terms: </label><br/>Mathematical Statistics <br/>الإحصاء الرياضي
<br/><br/><label>Subjects--Index Terms: </label>Generalized order statistics  Order statistics  Records  Single and product moments  Recurrence relations  Weibull-Weibull Distribution;Phani Distribution  Weibull Kumaraswamy distribution  The Power Inverted Topp–Leone Distribution  Characterization  إحصاءات الترتيب المعممة   إحصاءات الترتيب 
<br/><br/><label>Dewey Class. No.: </label>519.5