Balakrishnan N., Rao C.R. Order statistics. Applications

Elsevier, 1998. — 733 p.The area of Order Statistics received a tremendous attention from numerous researchers during the past century. During this period, several major theoretical advances were made in this area of research. As a matter of fact, two of those have been adjudged as breakthroughs in the field of Statistics [see: Kotz, S. and Johnson, N. L. (1991). Breakthroughs in Statistics, Vols. 1 and 2, Springer-Verlag, New York]. In the course of these developments, order statistics have also found important applications in many diverse areas including life-testing and reliability, robustness studies, statistical quality control, filtering theory, signal processing, image processing, and radar target detection.
Based on this immense activity, we decided to prepare this Handbook on Order Statistics and Their Applications. We feel that we have successfully brought together theoretical researchers working on theoretical and methodological advancements on order statistics and applied statisticians and engineers developing new and innovative applications of order statistics. Altogether, there are 44 articles covering most of the important theoretical and applied aspects of order statistics. For the convenience of readers, the subject matter has been divided into two volumes, the first one (Handbook-16, /file/1799261/, /file/1799262) focusing on Theory and Methods and the second one (Handbook-17, /file/1799276/, /file/1799277) dealing primarily with Applications. Each volume has also been organized according to different parts, with each part specializing on one aspect of Order Statistics.Part I. Results for Specific Distributions
Order Statistics in Exponential Distribution
Higher Order Moments of Order Statistics from Exponential and Right-truncated Exponential Distributions and Applications to Life-testing Problems
Log-gamma Order Statistics and Linear Estimation of Parameters
Recurrence Relations for Single and Product Moments of Order Statistics from a Generalized Logistic Distribution with Applications to Inference and Generalizations to Double Truncation
Order Statistics from the Type III Generalized Logistic Distribution and Applications
Part II. Linear Estimation
Estimation of Scale Parameter Based on a Fixed Set of Order Statistics
Optimal Linear Inference Using Selected Order Statistics in Location-Scale Models
L-Estimation
On Some L-estimation in Linear Regression Models
Part III. Inferential Methods
The Role of Order Statistics in Estimating Threshold Parameters
Parameter Estimation under Multiply Type-II Censoring
On Some Aspects of Ranked Set Sampling in Parametric Estimation
Some Uses of Order Statistics in Bayesian Analysis
Inverse Sampling Procedures to Test for Homogeneity in a Multinomial Distribution
Part IV. Prediction
Prediction of Order Statistics
Part V. Goodness-of-Fit Tests
The Probability Plot: Tests of Fit Based on the Correlation Coefficient
Distribution Assessment
Part VI. Applications
Application of Order Statistics to Sampling Plans for Inspection by Variables
Linear Combinations of Ordered Symmetric Observations with Applications to Visual Acuity
Order-Statistic Filtering and Smoothing of Time-Series: Part I
Order-Statistic Filtering and Smoothing of Time-Series: Part II
Order Statistics in Image Processing
Order Statistics Application to CFAR Radar Target Detection