Fourier Transforms of Distributions and Their Inverses

A Collection of Tables

Fritz Oberhettinger, Z. W. Birnbaum, E. Lukacs

• Publisher: Academic Press
• Year: 2014
• ISBN:
  9781483219028
• Topic: Mathématiques
• Subtopic: Probabilités et statistiques

Fourier Transforms of Distributions and Their Inverses: A Collection of Tables is a collection of tables on the integrals of Fourier transforms of distributions and their inverses involving the class of functions which are nonnegative and integrable over the interval. The emphasis is on the probability densities, and a number of examples are provided. This book is organized into two parts and begins with an introduction to those properties of characteristic functions which are important in probability theory, followed by a description of the tables and their use. The first three tables contain Fourier transforms of absolutely continuous distribution functions, namely, even functions (including Legendre functions); functions vanishing identically for negative values of the argument (including arbitrary powers); and functions that do not belong to either of the above classes. The transform pairs are numbered consecutively and arranged systematically according to the analytical character of the frequency function. The next two tables give the inverse transforms of the functions listed in the first and third tables, respectively. This monograph will appeal to students and specialists in the fields of probability and mathematical statistics.

Table of contents

• Front Cover
• Fourier Transforms of Distributions and Their Inverses: A Collection of Tables
• Copyright Page
• Table of Contents
• Preface
• Introduction
• PART I: TABLES OF FOURIER TRANSFORMS
• PART II: TABLES OF THE INVERSE TRANSFORMS OF PART I
• APPENDIX: DISTRIBUTION FUNCTIONS AND THEIR FOURIER TRANSFORMS FOUND IN THE STATISTICAL LITERATURE