A concept of generalized order statistics

Více o knize

Order statistics and record values play a crucial role in statistical applications, particularly in modeling and inference. This book introduces both well-known and new models of ordered random variables, applicable in areas such as reliability theory. Its primary aim is to present a concept of generalized order statistics, offering a unified approach to various models of ordered random variables. While numerous results on distributional and moment properties of order statistics exist in the literature, they are often treated separately. The generalized order statistics concept allows for a cohesive examination of structural similarities and analogies, enabling the subsumption and generalization of established results within a comprehensive framework. This approach yields a broad class of models with significant and practical properties for addressing real-world problems. Key topics covered include models of ordered random variables (including applications in reliability theory), order statistics with nonintegral sample sizes, sequential order statistics, record values, k-records, and more. Additionally, the book delves into generalized order statistics, their distribution theory, moment existence, characterization of distributions via moment sequences, recurrence relations, and inequalities for moments, along with reliability properties related to aging and partial ordering of generalized order statistics.