Stochastic methods
[For the first and third editions see Zbl 0357.60002 and Zbl 0665.60001, respectively.] The present book is an introduction to probability theory and statistics at the level of first or second year students at European Universities. There is more than enough material for a full one semester course whose objective is to teach the basic methodology of statistics through a carefully constructed introduction to probability theory. The eleven chapter headings (translated) are: discrete probability spaces; three basic methods of mathematical statistics (estimation, confidence intervals, tests); conditional probability, independence; moments (includes the weak law of large numbers); statistical inference of unknown probabilities; general probability theory (includes one- and multi-dimensional normal laws as well as \(\chi^ 2\), \(F\), \(t\) distributions); nonparametric statistics (includes rank statistics, Mann- Whitney-Wilcoxon test); regression analysis and analysis of variance; simulation (of samples, of random variables). A short list of statistical tables and a useful bibliography (with hints for further studies) complete the volume (which has a good index). The writing is clear and precise, the mathematical developments elementary but exact and readable. It is difficult to imagine a better and more useful book in German (or in any other language) for the subject matter at hand at the level aimed at. The authors have consistently used good German vocabulary for statistical terminology first introduced by English language authors. Thirty years ago, any introductory course in statistics in German was dogged by the problem of not having enough good German language texts to refer to. Of the 34 books mentioned by the present authors in their bibliography, there are only 4 in German devoted to statistics of which only one (the well-known text of Schmetterer at a more abstract level) covers most of the basic methods of statistics. The present volume is a welcome addition to the list of good and reliable introductory texts in statistics and accompanying probability theory.
scientific article; zbMATH DE number 706241