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Wolfgang Wertz I. The benefit of that method of estimation is made clear, especially, in the case of censored samples. The accompanying tables facilitate the application of that method. In chapters 11 and 12, the problems o r order statistics from exponential, rectangular, and gamma populations are lightly treated. The reader of such a book appreciates the painstaking editorial work of arranging, in one volume, independent treatises in a logically continuous way.
But such a volume is not free from the overlapping of some explanations and heterogeneity of the premises taken by each contributor concerning statistical backgrounds of the potential readers.
Also it may be said that students who intend to obtain a comprehensive study of order statistics from this book will be disappointed because he is referred to reference articles for the proofs of almost all funda- mental theorems. The book is not an introduction but rather a contribution to order statistics. Nevertheless, the reviewer would like to close the review of the book with the last phrase of H. There is no doubt, however, that the modern trend of applied statistics notably in industry is witnessing a growing use of methods based on ordered samples.
The publication of this first comprehensive treatise on the subject is therefore welcome and timely. The book is one of the Wiley Publications in Statistics.
The original version of the book was published in Polish in , the second revised edition in Polish w a s published in , simultaneously with its German translation. This English version, translated by R. Bartosznski as the third edition, contains a further extension and several changes.
A s can be expected from the past history of the book, on opening the pages those who a r e familiar with Western Litera- tures on the same subjects may feel a somewhat different flavor from the book.
This may come from the differences in emphasis. A s is described in Preface, the book was written with the purpose of giving a systematic introduction to modern probability theory and mathematical statistics. The first concern faced by the author is to decide in what detail these two subjects should be presented.
If the emphasis on these subjects is not well balanced, the title of a book should be named "Theory of Proba- bility," or "Mathematical Statistics," accordingly. Even if it is well balanced in their weights, there remains a risk of overdescription because there is abundant materials to be presented under these two subjects. At least as far as the number of pages is concerned, the book is almost equally divided into these two subjects, that is part I extends from page 1 to page and part II from page to the last page, In "Part I: Probability Theory," the author develops an explanation standing firmly on the frequency viewpoint of probability, leaving measure-theor etic considerations to the Supple- ment.
The description follows a usual way of presentation, deriving the fundamental probability distributions, giving a rather detailed explanation of limit theorems and then proceeding to a concise introduction to Markov chains.
Finally, the last chapter of part I which is devoted to stochastic processes, gives a lucid description of the subject. In this way, it should be said that part I is a very instructive and successful text on probability theory, especially for students majoring in statistics.
Statistics proper begins in "Part Mathematical Statistics. A short sketch of order statistics and the theory of runs is given in the following two chapters.
In the chapter on order statistics, it is interesting to find a rather extensive description of the relationship between the empirical distributions and the corre- sponding theoretical ones as is shown in the Glivenko Theorem and the Kolmogorov-Smirnov Theorem. Surely it may be instructive to stress the different attitudes to the problem which exist between the significance test developed by R.
Fisher and hypotheses testing developed by J. Neyman and E. But to make clear the substantial difference which might exist between these two schools and to give a legitimate evaluation of these two approaches, it must be indis- pensable to explain carefully the controversy concerning the foundation and interpretation of probability and never refers to other existing viewpoints, the reviewer is afraid that it might cause the readers confusion and misinterpretation to stress only the formal difference between significance tests and hypotheses testing.
In the chapter of estimation, point estimation is pre- sented in a traditional way and rather strong attention is paid to the efficiency of estimates by means of the Rao-Cramer inequality. Interval estimation is lightly touched. Recently, it has widely been recognized that the notion of sufficient statistics is very important and is powerful in both estimation and hypotheses testing.
But the reviewer is afraid to say that this book does not give a due evaluation to sufficient statistics. In the last chapter, chap. Each chapter is closed with some historical remarks on the theme. Maxwell, Methuen l , pp. Cox and Walter L. Smith, Methuen , pp. Stuart, Methuen , pp. Cox and Smith Related Papers.
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