TY  - BOOK
AU  - Khater Abd El Hameed Gadelrab Kenaway, 
AU  - Ali Ahmed Abdulrahman
AU  - Ibrahim B. Abdul-Moniem
AU  - Salwa Mahmoud Samy Assar
TI  - Some characterizations based on  generalized order statistics
U1  - 519.5 
PY  - 2025///
KW  - Mathematical Statistics
KW  - الإحصاء الرياضي
KW  - Generalized order statistics
KW  - Order statistics
KW  - Records
KW  - Single and product moments
KW  - Recurrence relations
KW  - Weibull-Weibull Distribution;Phani Distribution
KW  - Weibull Kumaraswamy distribution
KW  - The Power Inverted Topp–Leone Distribution
KW  - Characterization
KW  - إحصاءات الترتيب المعممة
KW  - إحصاءات الترتيب
N1  - Thesis (Ph.D)-Cairo University, 2025; Bibliography: pages 124-130; Issues also as CD
N2  - The characterizations based on generalized order statistics are crucial for 
theoretical advancements and practical applications across various fields. Their 
ability to provide detailed insights into the distributional properties of ordered 
data makes them indispensable tools for statisticians, engineers, data scientists, 
and researchers. Characterizations based on generalized order statistics deepen 
our understanding of the structural properties of ordered data. By extending 
classical results, generalized order statistics offer new insights into the behavior 
and relationships of statistical distributions. 
 This study explores some characterizations based on generalized order 
statistics from Weibull-Family of Life distributions, characterization based on 
recurrence relation for single moments of generalized order statistics, and 
characterization based on recurrence relation for product moments of 
generalized order statistics. 
 The study investigates some characterizations based on generalized order 
statistics for many distributions, the recurrence relation for single expectations 
of generalized order statistics, and moments of order statistics.  Additionally, it 
tackles L-moments, TL-momets, and upper record values, characterization based 
on recurrence relation for single moments of generalized order statistics, and 
characterization based on recurrence relation for product moments of generalized 
order statistics. Some computational results of the means and variances of order 
statistics are carried out based on theoretical results of order statistics for some 
sample sizes simply and efficiently. Special moments like L-moments and TL- 
moments, as well as the characterization of generalized order statistics, are also 
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.
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
ER  -