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Author: Uwe Küchler
Publisher: Springer Science & Business Media
ISBN: 0387227652
Category : Mathematics
Languages : en
Pages : 322
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Book Description
A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.
Author: Uwe Küchler
Publisher: Springer Science & Business Media
ISBN: 0387227652
Category : Mathematics
Languages : en
Pages : 322
Get Book
Book Description
A comprehensive account of the statistical theory of exponential families of stochastic processes. The book reviews the progress in the field made over the last ten years or so by the authors - two of the leading experts in the field - and several other researchers. The theory is applied to a broad spectrum of examples, covering a large number of frequently applied stochastic process models with discrete as well as continuous time. To make the reading even easier for statisticians with only a basic background in the theory of stochastic process, the first part of the book is based on classical theory of stochastic processes only, while stochastic calculus is used later. Most of the concepts and tools from stochastic calculus needed when working with inference for stochastic processes are introduced and explained without proof in an appendix. This appendix can also be used independently as an introduction to stochastic calculus for statisticians. Numerous exercises are also included.
Author: Uwe Kuchler
Publisher:
ISBN: 9781475770995
Category :
Languages : en
Pages : 336
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Book Description
Author: Uwe Küchler
Publisher:
ISBN:
Category :
Languages : en
Pages :
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Book Description
Author: U. Küchler
Publisher:
ISBN:
Category :
Languages : en
Pages : 40
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Book Description
Author: O. Barndorff-Nielsen
Publisher: John Wiley & Sons
ISBN: 1118857372
Category : Mathematics
Languages : en
Pages : 248
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Book Description
First published by Wiley in 1978, this book is being re-issued with a new Preface by the author. The roots of the book lie in the writings of RA Fisher both as concerns results and the general stance to statistical science, and this stance was the determining factor in the author's selection of topics. His treatise brings together results on aspects of statistical information, notably concerning likelihood functions, plausibility functions, ancillarity, and sufficiency, and on exponential families of probability distributions.
Author: Masafumi Akahira
Publisher: Springer
ISBN: 9811052964
Category : Mathematics
Languages : en
Pages : 122
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Book Description
This book presents new findings on nonregular statistical estimation. Unlike other books on this topic, its major emphasis is on helping readers understand the meaning and implications of both regularity and irregularity through a certain family of distributions. In particular, it focuses on a truncated exponential family of distributions with a natural parameter and truncation parameter as a typical nonregular family. This focus includes the (truncated) Pareto distribution, which is widely used in various fields such as finance, physics, hydrology, geology, astronomy, and other disciplines. The family is essential in that it links both regular and nonregular distributions, as it becomes a regular exponential family if the truncation parameter is known. The emphasis is on presenting new results on the maximum likelihood estimation of a natural parameter or truncation parameter if one of them is a nuisance parameter. In order to obtain more information on the truncation, the Bayesian approach is also considered. Further, the application to some useful truncated distributions is discussed. The illustrated clarification of the nonregular structure provides researchers and practitioners with a solid basis for further research and applications.
Author: Stefan Bedbur
Publisher: Springer Nature
ISBN: 3030819000
Category : Mathematics
Languages : en
Pages : 147
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Book Description
This book provides a concise introduction to exponential families. Parametric families of probability distributions and their properties are extensively studied in the literature on statistical modeling and inference. Exponential families of distributions comprise density functions of a particular form, which enables general assertions and leads to nice features. With a focus on parameter estimation and hypotheses testing, the text introduces the reader to distributional and statistical properties of multivariate and multiparameter exponential families along with a variety of detailed examples. The material is widely self-contained and written in a mathematical setting. It may serve both as a concise, mathematically rigorous course on exponential families in a systematic structure and as an introduction to Mathematical Statistics restricted to the use of exponential families.
Author: Ole Barndorff-Nielsen
Publisher:
ISBN: 9780835733915
Category :
Languages : en
Pages : 238
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Book Description
Author: Ole E. Barndorff-Nielsen
Publisher:
ISBN:
Category : Distribution (Probability theory)
Languages : en
Pages : 238
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Book Description
Author: V. Seshadri
Publisher: Oxford University Press on Demand
ISBN: 9780198522430
Category : Mathematics
Languages : en
Pages : 256
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Book Description
This book begins with a historical survey of `generalized inverse Gaussian laws', in which the wartime contribution of Etienne Halphen is presented for the first time. The inverse Gaussian distribution, its properties, and its implications are set in a wide perspective. The concepts of inversion and inverse natural exponential functions are presented, together with an analysis of the `Tweedie' scale, of which the Gaussian distribution is an important specialcase. Chapter 2 concerns the basic theory of exponential functions, focusing on the inverse Gaussian Law. Chapter 3 is devoted to various characterization results, while Chapter 4 is concerned with the construction of multivariate distributions, and the relationship to simplex distributions,combinations, and finite mixtures. Chapter 5 introduces the concept of inverse natural exponential functions and Chapter 6 presents useful statistical results. Up-to-date research is presented in the form of exercises, a special chapter on characterizations is included, and a summary of statistical issues concerning estimation and interference are provided. Research workers will find inspiration for further investigations.
