Fourier Transforms of Distributions and Their Inverses

Author: Fritz Oberhettinger
Publisher: Academic Press
ISBN: 148321902X
Format: PDF, Docs
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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.

The Spectral Analysis of Time Series

Author: Lambert Herman Koopmans
Publisher: Academic Press
ISBN:
Format: PDF, ePub, Mobi
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To tailor time series models to a particular physical problem and to follow the working of various techniques for processing and analyzing data, one must understand the basic theory of spectral (frequency domain) analysis of time series. This classic book provides an introduction to the techniques and theories of spectral analysis of time series. In a discursive style, and with minimal dependence on mathematics, the book presents the geometric structure of spectral analysis. This approach makes possible useful, intuitive interpretations of important time series parameters and provides a unified framework for an otherwise scattered collection of seemingly isolated results. The books strength lies in its applicability to the needs of readers from many disciplines with varying backgrounds in mathematics. It provides a solid foundation in spectral analysis for fields that include statistics, signal process engineering, economics, geophysics, physics, and geology. Appendices provide details and proofs for those who are advanced in math. Theories are followed by examples and applications over a wide range of topics such as meteorology, seismology, and telecommunications. Topics covered include Hilbert spaces; univariate models for spectral analysis; multivariate spectral models; sampling, aliasing, and discrete-time models; real-time filtering; digital filters; linear filters; distribution theory; sampling properties ofspectral estimates; and linear prediction. Key Features * Hilbert spaces * univariate models for spectral analysis * multivariate spectral models * sampling, aliasing, and discrete-time models * real-time filtering * digital filters * linear filters * distribution theory * sampling properties of spectral estimates * linear prediction

Mathematical basis of statistics

Author: Jean René Barra
Publisher: Academic Pr
ISBN:
Format: PDF, ePub, Docs
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Statistical spaces; Sufficiency and freedom; Statistical information; Statistical inference; Testing statistical hypotheses; Statistical estimation; The multivariate normal distribution; Random matrices; Linear normal statistical spaces; Exponential statistical spaces; Testing hypotheses on exponential statistical spaces; Functional analysis and mathematical statistics; Conditional probability.

Mathematical methods of statistical quality control

Author: Károly Sarkadi
Publisher:
ISBN:
Format: PDF, Docs
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Statistical methods of quality control. Probability theory and its role in the methods of statistical quality control. Theoretical foundations. Elements of probability theory. Random variables. Fundamentals of sampling. Fundamentals of mathematical statistics. Methods of statistical quality control. Statistical methods in the control of production processes. Acceptance sampling. Reliability theory.