Karl Mosler – författare

This book introduces a new representation of probability measures, the lift zonoid representation, and demonstrates its usefulness in statistical applica­ tions. The material divides into nine chapters. Chapter 1 exhibits the main idea of the lift zonoid representation and surveys the principal results of later chap­ ters without proofs. Chapter 2 provides a thorough investigation into the theory of the lift zonoid. All principal properties of the lift zonoid are col­ lected here for later reference. The remaining chapters present applications of the lift zonoid approach to various fields of multivariate analysis. Chap­ ter 3 introduces a family of central regions, the zonoid trimmed regions, by which a distribution is characterized. Its sample version proves to be useful in describing data. Chapter 4 is devoted to a new notion of data depth, zonoid depth, which has applications in data analysis as well as in inference. In Chapter 5 nonparametric multivariate tests for location and scale are in­ vestigated; their test statistics are based on notions of data depth, including the zonoid depth. Chapter 6 introduces the depth of a hyperplane and tests which are built on it. Chapter 7 is about volume statistics, the volume of the lift zonoid and the volumes of zonoid trimmed regions; they serve as multivariate measures of dispersion and dependency. Chapter 8 treats the lift zonoid order, which is a stochastic order to compare distributions for their dispersion, and also indices and related orderings.

A bibliography on stochastic orderings. Was there a real need for it? In a time of reference databases as the MathSci or the Science Citation Index or the Social Science Citation Index the answer seems to be negative. The reason we think that this bibliog­ raphy might be of some use stems from the frustration that we, as workers in the field, have often experienced by finding similar results being discovered and proved over and over in different journals of different disciplines with different levels of mathematical so­ phistication and accuracy and most of the times without cross references. Of course it would be very unfair to blame an economist, say, for not knowing a result in mathematical physics, or vice versa, especially when the problems and the languages are so far apart that it is often difficult to recognize the analogies even after further scrutiny. We hope that collecting the references on this topic, regardless of the area of application, will be of some help, at least to pinpoint the problem. We use the term stochastic ordering in a broad sense to denote any ordering relation on a space of probability measures. Questions that can be related to the idea of stochastic orderings are as old as probability itself. Think for instance of the problem of comparing two gambles in order to decide which one is more favorable.

Das Buch bietet eine Einführung in die wichtigsten Methoden der beschreibenden Statistik und ausgewählte Kapitel der Wirtschaftsstatistik, insbesondere in die Indexzahlen und die Messung von Konzentration und Disparität. Die Darstellung zielt auf klare Begriffe, nachvollziehbare Verfahren und Motivation aus den Wirtschaftswissenschaften.

Das Buch bietet eine Einführung in die wichtigsten Methoden der Wahrscheinlichkeitsrechnung und des statistischen Schließens, das heißt, der Schätzung von Parametern und des Testens von Hypothesen. Hinweise zur Durchführung der Verfahren am Computer mit Excel® und SPSS® ergänzen den Text.

Martin Beckmann is going to celebrate his sixtieth birthday. This is almost unbelievable considering the vitality, ingenuity, and activity which he continues to show as he always did. It is an honor­ able and pleasant duty for the whole economics community to show hirn the respect, gratitude, and affection which he deserves. Thus, those' who have contributed to this festschrift may be thought of as a dele­ gation from a much larger community in which all of us are joined; the editors in particular feel deeply connected with and enriched by the personality and scientific work of Martin Beckmann. Martin Beckmann is one of those rare scholars who are not narrow­ minded specialists in one field; he has been active in many areas of economics and operations research which rapidly developed since World War 11, and he has contributed original and fruitful ideas in almost all of them. The variety of topics treated in this volume aims to re­ flect the impressive width of his scientific interests.

Dieses Lehrbuch erklärt die Grundkonzepte der Datenanalyse sowie des statistischen Schätzens und Testens in kompakter Form. Die Darstellung zielt dabei auf eine klare Begriffsbildung und deren Begründung ab. So ist es ein Leichtes, sich das nötige Basiswissen über die Auswertung von Daten, den Umgang mit Wahrscheinlichkeiten und statistische Schlussweisen anzueignen. Zahlreiche Beispiele und Grafiken veranschaulichen die Begriffe. Das Buch richtet sich vornehmlich an Studierende der BWL und der technischen Disziplinen an Fachhochschulen und Universitäten. Es kann aber auch in allen anderen Gebieten zum Einsatz kommen, in denen statistische Methoden gebraucht werden.

Dieses Lehrbuch richtet sich an Studierende im Bachelor- und Masterstudium der wirtschaftswissenschaftlichen Fächer. Es soll die Studierenden in die Lage versetzen, ökonomische Texte zu verstehen und Optimierungsverfahren einzusetzen, und sie auch im gesamten Studium als Nachschlagewerk begleiten. Eine Besonderheit des Buches ist die enge Verknüpfung von mathematischen Begriffen mit solchen der Volkswirtschaftslehre und des Operations Research. Die Autoren legen dabei besonderen Wert auf die anschauliche Darstellung der relevanten Begriffe und Modelle. Vorausgesetzt wird das übliche Schulwissen in Mathematik; jedoch werden die inhaltlichen Schwerpunkte des Abiturs in knapper Form aufgegriffen und wiederholt. Zahlreiche Lernhilfen, durchgerechnete Beispiele und Aufgaben mit Kurzlösungen ermöglichen ein Selbststudium.

This book introduces main concepts and techniques, enables students to read economic texts, understand economic models and apply optimization methods. It accompanies students throughout their bachelor’s and master’s studies and serves as a reference book. Numerous learning aids, worked examples, and exercises with short solutions facilitate self-study. A special feature of the book is the close link between mathematical concepts and those of economics and operations research: To clarify the role of mathematical methods as part of the basic training in economics, production and utility functions are introduced early on, as are models of interest and growth of an economy. The prerequisite for this textbook is high school mathematics, including introductory courses on real functions and differential calculus as well as algebraic operations, trigonometric functions and analytical geometry. Appendices provide summaries of specific material for short reference.This book is a translation of the original German edition Mathematische Methoden für Ökonomen, 3rd edition, by Karl Mosler, Rainer Dyckerhoff and Christoph Scheicher, published by Springer-Verlag GmbH, DE in 2018. The translation was done with the help of an artificial intelligence machine translation tool. A subsequent human revision was done primarily in terms of content, so that the book will read stylistically differently from a conventional translation.