Generalized Gamma Convolutions And Related Classes Of Distributions And Densities
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Generalized Gamma Convolutions and Related Classes of Distributions and Densities
Author: Lennart Bondesson
language: en
Publisher: Springer Science & Business Media
Release Date: 2012-12-06
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.
Life Distributions
Author: Albert W. Marshall
language: en
Publisher: Springer Science & Business Media
Release Date: 2007-10-13
This book is devoted to the study of univariate distributions appropriate for the analyses of data known to be nonnegative. The book includes much material from reliability theory in engineering and survival analysis in medicine.
Probability
Author: Allan Gut
language: en
Publisher: Springer Science & Business Media
Release Date: 2013
Like its predecessor, this book starts from the premise that, rather than being a purely mathematical discipline, probability theory is an intimate companion of statistics. The book starts with the basic tools, and goes on to cover a number of subjects in detail, including chapters on inequalities, characteristic functions and convergence. This is followed by a thorough treatment of the three main subjects in probability theory: the law of large numbers, the central limit theorem, and the law of the iterated logarithm. After a discussion of generalizations and extensions, the book concludes with an extensive chapter on martingales. The new edition is comprehensively updated, including some new material as well as around a dozen new references.