Sharp Inequalities for Ordered Random Variables in Statistics and Reliability

Beschreibung

This second volume, similar to the first volume, discusses various inequalities and sharp bounds for some general forms of ordered data as well as some functions of them. In particular, different bounds and their sharpness are discussed for order statistics from identically distributed and exchangeable samples, order statistics from arbitrarily distributed variable, coherent and mixed reliability systems, record values and their extensions, generalized order statistics and finally mixtures of ordered distributions. An elaborate numerical evaluation and comparison of various bounds are also presented to illustrate their inherent differences and their accuracy and precision. Moreover, their applications to inference and reliability are also highlighted. This second and final volume provides an in-depth exposure to various mathematical inequalities and bounds established historically as well as in recent years and their applications to various forms of ordered data and some important functions of them like range, L-statistics and trimmed mean. It thus presents an up-to-date discussion of all results in this important area of mathematical and statistical research. The results described here are general and so would be useful in other areas of Probability and Statistics as well.

This second volume, similar to the first volume, discusses various inequalities and sharp bounds for some general forms of ordered data as well as some functions of them. In particular, different bounds and their sharpness are discussed for order statistics from identically distributed and exchangeable samples, order statistics from arbitrarily distributed variable, coherent and mixed reliability systems, record values and their extensions, generalized order statistics and finally mixtures of ordered distributions. An elaborate numerical evaluation and comparison of various bounds are also presented to illustrate their inherent differences and their accuracy and precision. Moreover, their applications to inference and reliability are also highlighted. This second and final volume provides an in-depth exposure to various mathematical inequalities and bounds established historically as well as in recent years and their applications to various forms of ordered data and some important functions of them like range, L-statistics and trimmed mean. It thus presents an up-to-date discussion of all results in this important area of mathematical and statistical research. The results described here are general and so would be useful in other areas of Probability and Statistics as well.

Autor*in

Narayanaswamy Balakrishnan

Themen in »Sharp Inequalities for Ordered Random Variables in Statistics and Reliability«

order statistics record values generalized order statistics progressively censored type II order statistics ageing models kth records reliability systems, mixtures of ordered distributions sharp bounds attainability conditions restricted families of Distributions

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