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Let a sample of size n from a specified or unspecified population be arranged in nondecreasing order. Then the ordered sample values are collectively called the order statistics (plural) of the sample. In another sense of the expression, order statistics (singular) is that branch of the subject of statistics which deals with the mathematical properties of order statistics (plural) and with statistical methods based upon them. The majority of publications on order statistics deal with the order statistics of specific populations, and many of them involve the use of the sample order statistics to estimate one or more population parameters. The compiler of this bibliography makes a sharp distinction between order statistics and rank statistics, which is a branch of nonparametric statistics. Publications dealing with the ranks of the observations in the sample but not with the values (or expected values) of any of them will not in general be included in this bibliography; however, a few that are needed for comparison of methods based on ranks with alternatives based on order statistics will be included. Similarly, although the method of least squares is not based on order statistics, a substantial number of publications on least squares will be included because most alternative methods are based on order statistics and comparisons with the classical method of least squares are inevitable.
This volume provides an up-to-date coverage of the theory and applications of ordered random variables and their functions. Furthermore, it develops the distribution theory of OS systematically. Applications include procedures for the treatment of outliers and other data analysis techniques. Even when chapter and section headings are the same as in OSII, there are appreciable changes, mostly additions, with some obvious deletions. Parts of old Ch. 7, for example, are prime candidates for omission. Appendices are designed to help collate tables, computer algorithms, and software, as well as to compile related monographs on the subject matter. Extensive exercise sets will continue, many of them replaced by newer ones.
The literature on order statistics and inferenc eis quite extensive and covers a large number of fields ,but most of it is dispersed throughout numerous publications. This volume is the consolidtion of the most important results and places an emphasis on estimation. Both theoretical and computational procedures are presented to meet the needs of researchers, professionals, and students. The methods of estimation discussed are well-illustrated with numerous practical examples from both the physical and life sciences, including sociology,psychology,a nd electrical and chemical engineering. A complete, comprehensive bibliography is included so the book can be used both aas a text and reference.