An Introduction to Order Statistics

ISBN-13: 9789491216824 / Angielski / Twarda / 2013 / 244 str.

Mohammad Ahsanullah; Valery Nevzorov; Mohammad Shakil

Opis

This book presents the theory of order statistics in a way, such that beginners can get easily acquainted with the very basis of the theory without having to work through heavily involved techniques. At the same time more experienced readers can check their level of understanding and polish their knowledge with certain details. This is achieved by, on the one hand, stating the basic formulae and providing many useful examples to illustrate the theoretical statements, while on the other hand an upgraded list of references will make it easier to gain insight into more specialized results. Thus this book is suitable for a readership working in statistics, actuarial mathematics, reliability engineering, meteorology, hydrology, business economics, sports analysis and many more.

Recenzje

From the reviews:

"The theory is grouped in 21 chapters, in an interesting presentation. Thus, each chapter begins with a short exposition of the basic definitions and fundamental results corresponding to the studied problem; then, the readers are urged to solve a lot of exercises. ... The readers can find detailed solutions at the end of each chapter. These solutions are carefully written and filled with suitable remarks. ... The reading of the book is pleasant." (Eugen Paltanea, zbMATH, Vol. 1276, 2014)

Spis treści

Basic definitions.- Distributions of order statistics.- Sample quantiles and ranges.- Representations for order statistics.- Conditional distributions of order statistics.-Order statistics for discrete distributions.- Moments of order statistics: general relations.- Moments of uniform and exponential order statistics.- Moment relations for order statistics: normal distribution.- Asymptotic behavior of the middle and intermediate order statistics.- Asymptotic behavior of the extreme order statistics.- Some properties of estimators based on order statistics.- Minimum variance linear unbiased estimators.- Minimum variance linear unbiased estimators and predictors based on censored samples.- Estimation of parameters based on fixed number of sample quantiles.- Order statistics from extended samples.- Order statistics and record values.- Characterizations of distributions based on properties of order statistics.- Order statistics and record values based on Fα distributions.- Generalized order statistics.- Compliments and problems.

O autorze

V. B. Nevzorov, PhD, DS, is Professor of Probability and Statistics at St. Petersburg State University in St. Petersburg, Russia.