Some characterizations based on generalized order statistics /
Khater Abd El Hameed Gadelrab Kenaway,
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.
Thesis (Ph.D)-Cairo University, 2025.
Bibliography: pages 124-130.
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
Text in English and abstract in Arabic & English.
Mathematical Statistics
الإحصاء الرياضي
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
519.5
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.
Thesis (Ph.D)-Cairo University, 2025.
Bibliography: pages 124-130.
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
Text in English and abstract in Arabic & English.
Mathematical Statistics
الإحصاء الرياضي
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
519.5