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Titlebook: Generalized Gamma Convolutions and Related Classes of Distributions and Densities; Lennart Bondesson Book 1992 Springer-Verlag New York, I

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书目名称Generalized Gamma Convolutions and Related Classes of Distributions and Densities
编辑Lennart Bondesson
视频video
丛书名称Lecture Notes in Statistics
图书封面Titlebook: Generalized Gamma Convolutions and Related Classes of Distributions and Densities;  Lennart Bondesson Book 1992 Springer-Verlag New York, I
描述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 application
出版日期Book 1992
关键词Finite; convolution; distribution; function; theorem; variable
版次1
doihttps://doi.org/10.1007/978-1-4612-2948-3
isbn_softcover978-0-387-97866-6
isbn_ebook978-1-4612-2948-3Series ISSN 0930-0325 Series E-ISSN 2197-7186
issn_series 0930-0325
copyrightSpringer-Verlag New York, Inc. 1992
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发表于 2025-3-21 23:15:52 | 显示全部楼层
https://doi.org/10.1057/9781137559173e probability material can be found in e.g. Feller’s (1971) book. The chapter serves the purpose of giving the background. It also makes it possible to emphasize certain aspects and to fix the terminology. Pick functions are treated in Section 2.4. Since these functions are not well known to probabi
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https://doi.org/10.1057/9781137264671 by 0. Thorin in 1977 as a useful tool for proving ID of particular distributions. This class of distributions, in honor of Thorin often called the ℐ-class, also has its own interest. It is the smallest class of distributions on ℝ. that contains the Gamma distributions and is closed with respect to
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Conscience and Freedom of Consciencedistribution with mgf exp·s./2× is a simple example of such a distribution. An extension of ℐ to a class of distributions on the whole real line ℝ is thus desirable. This chapter is devoted to the class ℐ. of extended generalized Gamma convolutions (EGGC) introduced by Thorin (1978a).
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Empirische Grundlagen der Fallstudien,., this being the discrete analogue of ℐ. The analogue of the Gamma distribution is the Negative Binomial distribution. By a . ., we mean a limit distribution for a sequence of finite convolutions of Negative Binomial distributions. The class of GNBC’s is denoted ℐ.. Many of the results valid for ℐ
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Extended Generalized Gamma Convolutions,distribution with mgf exp·s./2× is a simple example of such a distribution. An extension of ℐ to a class of distributions on the whole real line ℝ is thus desirable. This chapter is devoted to the class ℐ. of extended generalized Gamma convolutions (EGGC) introduced by Thorin (1978a).
发表于 2025-3-23 04:59:10 | 显示全部楼层
,Introduction: Conrad’s Sensational Women,In Chapter 3 the distributions in ℐ were studied through the mgf. In this chapter we look at densities of GGC’s and their properties. In particular, classes of densities in ℐ are in focus. Some rather surprising results appear.
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