Showing papers on "Infinite divisibility published in 1977"
TL;DR: In this article, it was shown that any mixture of the r-dimensional normal distributions determined by setting ~ = # + 2 f i A and X=a2A (2) and letting o -2 follow the distribution (1) is infinitely divisible.
Abstract: (~'/z)~/2 x~-le --~':~-~+~ (x>0) , (1) 2 K ~ ( ] / ~ ) has the property of infinite divisibility. It follows simply from this that any mixture of the r-dimensional normal distributions Nr(~, X) determined by setting ~ = # + ~ 2 f i A and X=a2A (2) and letting o -2 follow the distribution (1) is infinitely divisible; here #, fl and A are new parameters, # and fi being r-dimensional vectors while 3 is a positive definite r x r matrix with determinant IA I = 1. This class of mixtures includes the r-dimensional hyperbolic distribution
278 citations
TL;DR: In this article, the authors model the creep of concrete as a process with independent increments of locally gamma distribution and transform it to a stationary gamma process, and use Monte Carlo simulations to determine process parameters from creep test data.
Abstract: Creep of concrete is modeled as a process with independent increments of locally gamma distribution. The process is transformed to a stationary gamma process. The mean prediction agrees with the deterministic double power law established previously. Infinite divisibility of the increment distribution is assumed. This is justified by additivity of deformations and of stresses, and also by considerations of the microscopic mechanism of creep, assuming creep to be due to migrations of widely spaced solid particles along micropore passages whose length is statistically distributed. The treatment of creep as a stochastic process allows extracting considerable information from measurements even on one specimen, although a greater number of specimens is preferable. The main use of the model is in extrapolation of short time creep data into long times, and calculation of confidence limits. Methods of determining process parameters from creep test data are given. Monte Carlo simulations demonstrate reasonable agreement with test data.
175 citations
TL;DR: In this article, it was shown that the lognormal distribution is the weak limit of a sequence of probability distributions all of which are generalized Γ-convolutions and thus infinitely divisible.
Abstract: Summary In the present paper the author proves that the lognormal distribution is infinitely divisible. This is achieved by showing that the lognormal is the weak limit of a sequence of probability distributions all of which are generalized Γ-convolutions and thus infinitely divisible. It is also proved that the lognormal itself is a generalized Γ-convolution.
171 citations
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.
Abstract: Necessary and sufficient conditions are given for a distribution function in ℝ2 to be max-infinitely divisible. The d.f. F is max i.d. if F t is a d.f. for every t > 0. This property is essential in defining multivariate extremal processes and arises in an approach to the study of the range of an i.i.d. sample.
137 citations
TL;DR: In this paper, the authors investigated the Pareto distribution more closely and proved that it belongs to a well-known subclass of the class of infinitely divisible distributions, the so-called class L.
Abstract: Summary That the Pareto distribution is infinitely divisible is a simple consequence of an important theorem by Goldie and Steutel if an observation by Thyrion is used. In the present paper the author investigates the Pareto distribution more closely and proves that it belongs to a well-known subclass of the class of infinitely divisible distributions, the so called class L. That is achieved by showing that the Pareto distribution can be viewed as a “generalized Γ-convolution”. The corresponding problem concerning the lognormal distribution is briefly touched upon.
80 citations
01 Sep 1977
39 citations
26 citations
01 Sep 1977
10 citations
TL;DR: In this paper, the authors give a positive answer to the question "if X"@a is @?-distributed of order @a, and X" @b of order@b, with X'@a and X''@b independent, is X" "@aX"@b infinitely divisible?'' This question, posed by Steutel in Ref.
9 citations
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TL;DR: In this paper, the idea of confined quarks or partons as constituents of the elementary particles was already present in the Greek atomic theory, and it was suggested that in both cases the idea is in large part a response to an inherent conflict between the intuitive notion of infinite divisibility and the notion of discrete fundamental atoms of matter.
Abstract: We point out that the idea of confined quarks or partons as constituents of the elementary particles was already present in the Greek atomic theory. We describe some similarities and differences between ancient and modern confinement, and we suggest that in both cases the idea is in large part a response to an inherent conflict between the intuitive notion of infinite divisibility and the idea of discrete fundamental atoms of matter.
5 citations
01 Jan 1977
TL;DR: The final author version and the galley proof are versions of the publication after peer review and the final published version features the final layout of the paper including the volume, issue and page numbers.
Abstract: • A submitted manuscript is the author's version of the article upon submission and before peer-review. There can be important differences between the submitted version and the official published version of record. People interested in the research are advised to contact the author for the final version of the publication, or visit the DOI to the publisher's website. • The final author version and the galley proof are versions of the publication after peer review. • The final published version features the final layout of the paper including the volume, issue and page numbers.