Statistical Properties Of The Generalized Inverse Gaussian Distribution
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Statistical Properties Of The Generalized Inverse Gaussian Distribution
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Author : B. Jorgensen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Statistical Properties Of The Generalized Inverse Gaussian Distribution written by B. Jorgensen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
In 1978 the idea of studying the generalized inverse Gaussian distribution was proposed to me by Professor Ole Barndorff-Nielsen, who had come across the distribution in the study of the socalled hyperbolic distributions where it emerged in connection with the representation of the hyperbolic distributions as mixtures of normal distributions. The statistical properties of the generalized inverse Gaussian distribution were at that time virtually unde veloped, but it turned out that the distribution has some nice properties, and models many sets of data satisfactorily. This work contains an account of the statistical properties of the distribu tion as far as they are developed at present. The work was done at the Department of Theoretical Statistics, Aarhus University, mostly in 1979, and was partial fulfilment to wards my M. Sc. degree. I wish to convey my warm thanks to Ole Barn dorff-Nielsen and Preben BI~sild for their advice and for comments on earlier versions of the manuscript and to Jette Hamborg for her skilful typing.
Statistical Properties Of The Generalized Inverse Gaussian Distribution
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Author : Bent Jørgensen
language : en
Publisher: Springer
Release Date : 2012-10-20
Statistical Properties Of The Generalized Inverse Gaussian Distribution written by Bent Jørgensen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-10-20 with Mathematics categories.
Statistical Properties Of The Generalized Inverse Gaussian Distribution
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Author : Bent Jørgensen
language : en
Publisher:
Release Date : 1980
Statistical Properties Of The Generalized Inverse Gaussian Distribution written by Bent Jørgensen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with Gaussian distribution categories.
Memoirs
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Author :
language : en
Publisher:
Release Date : 1980
Memoirs written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1980 with categories.
The Inverse Gaussian Distribution
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Author : V. Seshadri
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
The Inverse Gaussian Distribution written by V. Seshadri and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is written in the hope that it will serve as a companion volume to my first monograph. The first monograph was largely devoted to the probabilistic aspects of the inverse Gaussian law and therefore ignored the statistical issues and related data analyses. Ever since the appearance of the book by Chhikara and Folks, a considerable number of publications in both theory and applications of the inverse Gaussian law have emerged thereby justifying the need for a comprehensive treatment of the issues involved. This book is divided into two sections and fills up the gap updating the material found in the book of Chhikara and Folks. Part I contains seven chapters and covers distribution theory, estimation, significance tests, goodness-of-fit, sequential analysis and compound laws and mixtures. The first part forms the backbone of the theory and wherever possible I have provided illustrative examples for easy assimilation of the theory. The second part is devoted to a wide range of applications from various disciplines. The applied statistician will find numerous instances of examples which pertain to a first passage time situation. It is indeed remarkable that in the fields of life testing, ecology, entomology, health sciences, traffic intensity and management science the inverse Gaussian law plays a dominant role. Real life examples from actuarial science and ecology came to my attention after this project was completed and I found it impossible to include them.
The Inverse Gaussian Distribution
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Author : Raj Chhikara
language : en
Publisher: CRC Press
Release Date : 2024-11-01
The Inverse Gaussian Distribution written by Raj Chhikara and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2024-11-01 with Mathematics categories.
This monograph is a compilation of research on the inverse Gaussian distribution. It emphasizes the presentation of the statistical properties, methods, and applications of the two-parameter inverse Gaussian family of distribution. It is useful to statisticians and users of statistical distribution.
Advances In Order Restricted Statistical Inference
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Author : Richard Dykstra
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Advances In Order Restricted Statistical Inference written by Richard Dykstra and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
With support from the University of Iowa and the Office of Naval Research. a small conference on order restricted inference was held at the University of Iowa in Iowa City in April of 1981. There were twenty-one participants. mostly from the midwest. and eleven talks were presented. A highlight of the conference was a talk by D. J. Bartholomew on. "Reflections on the past and thoughts about the future. " The conference was especially valuable because it brought together researchers who were thinking about related problems. A small conference on a limited topic is one of the best ways to stimulate research and facilitate collaboration. Because of the success of the first conference. a second conference was organized and held in September of 1985. This second conference was made possible again by support from the Office of Naval Research under Department of the Navy Contract NOOOI4-85-0161 and the University of Iowa. There were thirty-five participants and twenty presentations on a wide variety of topics dealing with order restricted inference at the second conference. This volume is a collection of fourteen of those presentations. By collecting together and organizing the fundamental results in order restricted inference in Statistical Inference under Order Restrictions. R. E. Barlow. D. J. Bartholomew. J. M. Bremner and H. D. Brunk have done much to stimulate research in this area. and so we wish to express our gratitude to them first.
Topics In Statistical Information Theory
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Author : Solomon Kullback
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01
Topics In Statistical Information Theory written by Solomon Kullback and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.
The relevance of information theory to statistical theory and its applications to stochastic processes is a unifying influence in these TOPICS. The integral representation of discrimination information is presented in these TOPICS reviewing various approaches used in the literature, and is also developed herein using intrinsically information-theoretic methods. Log likelihood ratios associated with various stochastic processes are computed by an application of minimum discrimination information estimates. Linear discriminant functionals are used in the information-theoretic analysis of a variety of stochastic processes. Sections are numbered serially within each chapter, with a decimal notation for subsections. Equations, examples, theorems and lemmas, are numbered serially within each section with a decimal notation. The digits to the left of the decimal point represent the section and the digits to the right of the decimal point the serial number within the section. When reference is made to a section, equation, example, theorem or lemma within the same chapter only the section number or equation number, etc., is given. When the reference is to a section ,equation, etc., in a different chapter, then in addition to the section or equation etc., number, the chapter number is also given. References to the bibliography are by the author's name followed by the year of publication in parentheses. The transpose of a matrix is denoted by a prime; thus one-row matrices are denoted by primes as the transposes of one-column matrices (vectors).
Parametric Statistical Models And Likelihood
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Author : Ole E Barndorff-Nielsen
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Parametric Statistical Models And Likelihood written by Ole E Barndorff-Nielsen and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This book is a slightly revised and expanded version of a set I I I of notes used for a lecture series given at the Ecole dlEte de I Probabilites at st. Flour in August 1986. In view of the statistical nature of the material discussed herein it was agreed to publish the material as a separate volume in the statistics series rather than, as is the tradition, in a joint volume in the Lecture Notes in Mathematics Series. It is a genuine pleasure to have this opportunity to thank I I I the organizers of Les Ecoles dlEte, and in particular Professor P. -L. Hennequin, for the excellent arrangements of these Summer Schools which form a very significant forum for the exchange of scientific ideas relating to probability. The efficient, careful and patient preparation of the typescript by Oddbj~rg Wethelund is also gratefully acknowledged. Aarhus, June 1988 O. E. Barndorff-Nielsen Parametric statistical Models and Likelihood O. E. Barndorff-Nielsen o. Introduction 0. 1. Outline of contents 1 0. 2. A few preliminaries 2 1. Likelihood and auxiliary statistics 1. 1. Likelihood 4 1. 2. Moments and cumulants of log likelihood derivatives 10 1. 3. Parametrization invariance 13 1. 4. Marginal and conditional likelihood 15 * 1. 5. Combinants, auxiliaries, and the p -model 19 1. 6. Orthogonal parameters 27 1. 7. Pseudo likelihood, profile likelihood and modified 30 profile likelihood 1. 8. Ancillarity and conditionality 33 41 1. 9. Partial sufficiency and partial ancillarity 1. 10.
Asymptotic Expansions For General Statistical Models
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Author : Johann Pfanzagl
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-27
Asymptotic Expansions For General Statistical Models written by Johann Pfanzagl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-11-27 with Mathematics categories.
0.1. The aim of the book Our "Contributions to a General Asymptotic Statistical Theory" (Springer Lecture Notes in Statistics, Vol. 13, 1982, called "Vol. I" in the following) suggest to describe the local structure of a general family ~ of probability measures by its tangent space, and the local behavior of a functional K: ~ ~~k by its gradient. Starting from these basic concepts, asymptotic envelope power functions for tests and asymptotic bounds for the concentration of estimators are obtained, and heuristic procedures are suggested for the construction of test- and estimator-sequences attaining these bounds. In the present volume, these asymptotic investigations are carried one step further: From approximations by limit distributions to approximations by Edgeworth expansions, 1 2 adding one term (of order n- / ) to the limit distribution. As in Vol. I, the investigation is "general" in the sense of dealing with arbitrary families of probability measures and arbitrary functionals. The investigation is special in the sense that it is restricted to statistical procedures based on independent, identically distributed observations. 2 Moreover, it is special in the sense that its concern are "regular" models (i.e. families of probability measures and functionals which are subject to certain general conditions, like differentiability). Irregular models are certainly of mathematical interest. Since they are hardly of any practical relevance, it appears justifiable to exclude them at this stage of the investigation.