Open Access
with Random Sample Size
TLDR
In this article, a class of probability generating functions for N, the sample size, and a NaS condition that implies the convergence to an ID (MID) law by convergence to a ϕ-ID (ϕ)-MID law and vise versa are discussed.Abstract:
Infinitely divisible (ID) and max-infinitely divisible (MID) laws are studied when the sample size is random. ϕ-ID and ϕ-MID laws introduced and studied here approximate random sums and random maximums. The main contributions in this study are: (i) in discussing a class of probability generating functions for N, the sample size, (ii) a NaS condition that implies the convergence to an ID (MID) law by the convergence to a ϕ-ID (ϕ-MID) law and vise versa and thus a discussion of attraction and partial attraction for ϕ-ID and ϕ-MID laws.read more
References
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Journal ArticleDOI
An Introduction to Probability Theory and Its Applications
David A. Freedman,William Feller +1 more
Journal ArticleDOI
Modeling asset returns with alternative stable distributions
TL;DR: In this article, the authors adopt a more fundamental view and extend the concept of stability to a variety of probabilistic schemes, which give rise to alternative stable distributions, which they compare empirically using S&P 500 stock return data.
Book
Random Summation: Limit Theorems and Applications
TL;DR: In this article, the authors considered the problem of growing random sum distributions in the Double Array Scheme Transfer Theorem and provided sufficient and sufficient conditions for the convergence of Random Sums of Independent Identically Distributed Random Variables.
Journal ArticleDOI
Max-infinite divisibility
A. A. Balkema,Sidney I. Resnick +1 more
TL;DR: In this paper, necessary and sufficient conditions for a distribution function in ℝ2 to be max-infinitely divisible are given for a multivariate extremal process and an approach to the study of the range of an i.i.d. sample.
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