Monotonicity Properties Of Infinitely Divisible Distributions
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Monotonicity Properties Of Infinitely Divisible Distributions
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Author : B. G. Hansen
language : en
Publisher:
Release Date : 1990
Monotonicity Properties Of Infinitely Divisible Distributions written by B. G. Hansen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1990 with Distribution (Probability theory). categories.
Monotonicity Properties Of Infinitely Divisible Distributions
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Author : Bjørn Gårn Hansen
language : en
Publisher:
Release Date : 1988
Monotonicity Properties Of Infinitely Divisible Distributions written by Bjørn Gårn Hansen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Distribution (Probability theory) categories.
Infinite Divisibility Of Probability Distributions On The Real Line
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Author : Fred W. Steutel
language : en
Publisher: CRC Press
Release Date : 2003-10-03
Infinite Divisibility Of Probability Distributions On The Real Line written by Fred W. Steutel and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-10-03 with Mathematics categories.
Infinite Divisibility of Probability Distributions on the Real Line reassesses classical theory and presents new developments, while focusing on divisibility with respect to convolution or addition of independent random variables. This definitive, example-rich text supplies approximately 100 examples to correspond with all major chapter topics and reviews infinite divisibility in light of the central limit problem. It contrasts infinite divisibility with finite divisibility, discusses the preservation of infinite divisibility under mixing for many classes of distributions, and investigates self-decomposability and stability on the nonnegative reals, nonnegative integers, and the reals.
Monotonicity Properties Of Infinitely Divisible Distributions
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Author : Björn Garn Hansen
language : fr
Publisher:
Release Date : 1988
Monotonicity Properties Of Infinitely Divisible Distributions written by Björn Garn Hansen and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Distribution (Probability theory) categories.
Probability In Banach Spaces 8 Proceedings Of The Eighth International Conference
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Author : R.M. Dudley
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Probability In Banach Spaces 8 Proceedings Of The Eighth International Conference written by R.M. Dudley 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.
Probability limit theorems in infinite-dimensional spaces give conditions un der which convergence holds uniformly over an infinite class of sets or functions. Early results in this direction were the Glivenko-Cantelli, Kolmogorov-Smirnov and Donsker theorems for empirical distribution functions. Already in these cases there is convergence in Banach spaces that are not only infinite-dimensional but nonsep arable. But the theory in such spaces developed slowly until the late 1970's. Meanwhile, work on probability in separable Banach spaces, in relation with the geometry of those spaces, began in the 1950's and developed strongly in the 1960's and 70's. We have in mind here also work on sample continuity and boundedness of Gaussian processes and random methods in harmonic analysis. By the mid-70's a substantial theory was in place, including sharp infinite-dimensional limit theorems under either metric entropy or geometric conditions. Then, modern empirical process theory began to develop, where the collection of half-lines in the line has been replaced by much more general collections of sets in and functions on multidimensional spaces. Many of the main ideas from probability in separable Banach spaces turned out to have one or more useful analogues for empirical processes. Tightness became "asymptotic equicontinuity. " Metric entropy remained useful but also was adapted to metric entropy with bracketing, random entropies, and Kolchinskii-Pollard entropy. Even norms themselves were in some situations replaced by measurable majorants, to which the well-developed separable theory then carried over straightforwardly.
Generalized Gamma Convolutions And Related Classes Of Distributions And Densities
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Author : Lennart Bondesson
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Generalized Gamma Convolutions And Related Classes Of Distributions And Densities written by Lennart Bondesson 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.
Generalized Gamma convolutions were introduced by Olof Thorin in 1977 and were used by him to show that, in particular, the Lognormal distribution is infinitely divisible. After that a large number of papers rapidly appeared with new results in a somewhat random order. Many of the papers appeared in the Scandinavian Actuarial Journal. This work is an attempt to present the main results on this class of probability distributions and related classes in a rather logical order. The goal has been to be on a level that is not too advanced. However, since the field is rather technical, most readers will find difficult passages in the text. Those who do not want to visit a mysterious land situated between the land of probability theory and statistics and the land of classical analysis should not look at this work. When some years ago I submitted a survey to a journal it was suggested by the editor, K. Krickeberg, that it should be expanded to a book. However, at that time I was rather reluctant to do so since there remained so many problems to be solved or to be solved in a smoother way than before. Moreover, there was at that time some lack of probabilistic interpretations and applications. Many of the problems are now solved but still it is felt that more applications than those presented in the work could be found.
Stochastic Orders And Applications
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Author : Karl Mosler
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Stochastic Orders And Applications written by Karl Mosler 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.
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.
Unimodality Of Probability Measures
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Author : Emile M.J. Bertin
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Unimodality Of Probability Measures written by Emile M.J. Bertin 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 2013-04-17 with Mathematics categories.
The central theme of this monograph is Khinchin-type representation theorems. An abstract framework for unimodality, an example of applied functional analysis, is developed for the introduction of different types of unimodality and the study of their behaviour. Also, several useful consequences or ramifications tied to these notions are provided. Being neither an encyclopaedia, nor a historical overview, this book aims to serve as an understanding of the basic features of unimodality. Chapter 1 lays a foundation for the mathematical reasoning in the chapters following. Chapter 2 deals with the concept of Khinchin space, which leads to the introduction of beta-unimodality in Chapter 3. A discussion on several existing multivariate notions of unimodality concludes this chapter. Chapter 4 concerns Khinchin's classical unimodality, and Chapter 5 is devoted to discrete unimodality. Chapters 6 and 7 treat the concept of strong unimodality on R and to Ibragimov-type results characterising the probability measures which preserve unimodality by convolution, and the concept of slantedness, respectively. Most chapters end with comments, referring to historical aspects or supplying complementary information and open questions. A practical bibliography, as well as symbol, name and subject indices ensure efficient use of this volume. Audience: Both researchers and applied mathematicians in the field of unimodality will value this monograph, and it may be used in graduate courses or seminars on this subject too.
Synergies Of Soft Computing And Statistics For Intelligent Data Analysis
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Author : Rudolf Kruse
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-07
Synergies Of Soft Computing And Statistics For Intelligent Data Analysis written by Rudolf Kruse 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 2012-09-07 with Computers categories.
In recent years there has been a growing interest to extend classical methods for data analysis. The aim is to allow a more flexible modeling of phenomena such as uncertainty, imprecision or ignorance. Such extensions of classical probability theory and statistics are useful in many real-life situations, since uncertainties in data are not only present in the form of randomness --- various types of incomplete or subjective information have to be handled. About twelve years ago the idea of strengthening the dialogue between the various research communities in the field of data analysis was born and resulted in the International Conference Series on Soft Methods in Probability and Statistics (SMPS). This book gathers contributions presented at the SMPS'2012 held in Konstanz, Germany. Its aim is to present recent results illustrating new trends in intelligent data analysis. It gives a comprehensive overview of current research into the fusion of soft computing methods with probability and statistics. Synergies of both fields might improve intelligent data analysis methods in terms of robustness to noise and applicability to larger datasets, while being able to efficiently obtain understandable solutions of real-world problems.
L Vy Processes And Infinitely Divisible Distributions
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Author : Sato Ken-Iti
language : en
Publisher: Cambridge University Press
Release Date : 1999
L Vy Processes And Infinitely Divisible Distributions written by Sato Ken-Iti and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Distribution (Probability theory) categories.