scholarly journals The domain of partial attraction of a Poisson law

1991 ◽  
Vol 4 (1) ◽  
pp. 169-190 ◽  
Author(s):  
Sándor Csörgő ◽  
Rossitza Dodunekova
Keyword(s):  
Poisson Law ◽  
Domain Of Partial Attraction

On a generalization of the Rényi–Srivastava characterization of the Poisson law

2021 ◽  
Vol 58 (1) ◽  
pp. 68-82
Author(s):  
Jean-Renaud Pycke
Keyword(s):  
Life Insurance ◽  
Collective Model ◽  
New Method ◽  
Bell Polynomials ◽  
Explicit Formulas ◽  
Compound Distributions ◽  
Poisson Law ◽  
Pierre Loti

AbstractWe give a new method of proof for a result of D. Pierre-Loti-Viaud and P. Boulongne which can be seen as a generalization of a characterization of Poisson law due to Rényi and Srivastava. We also provide explicit formulas, in terms of Bell polynomials, for the moments of the compound distributions occurring in the extended collective model in non-life insurance.

scholarly journals Extreme Value Theory for Hurwitz Complex Continued Fractions

Entropy ◽  
2021 ◽  
Vol 23 (7) ◽  
pp. 840
Author(s):  
Maxim Sølund Kirsebom
Keyword(s):  
Invariant Measure ◽  
Extreme Value Theory ◽  
Continued Fractions ◽  
Continued Fraction ◽  
Value Theory ◽  
Extreme Value ◽  
Poisson Law ◽  
Complex Continued Fractions

The Hurwitz complex continued fraction is a generalization of the nearest integer continued fraction. In this paper, we prove various results concerning extremes of the modulus of Hurwitz complex continued fraction digits. This includes a Poisson law and an extreme value law. The results are based on cusp estimates of the invariant measure about which information is still limited. In the process, we obtained several results concerning the extremes of nearest integer continued fractions as well.

scholarly journals On the asymptotic expansion of the remainder term in the case of convergence to the Poisson law

1962 ◽  
Vol 2 (1) ◽  
pp. 35-48
Author(s):  
B. Grigelionis
Keyword(s):  
Asymptotic Expansion ◽  
Remainder Term ◽  
Poisson Law

The abstracts (in two languages) can be found in the pdf file of the article. Original author name(s) and title in Russian and Lithuanian: Б. Григелионис, Об асимптотическом разложении остаточного члена в случае сходимости к закону Пуассона B. Grigelionis. Apie liekamojo nario asimptotinj išdėstymą konvergencijos į Puasono dėsnį atveju

scholarly journals On domains of partial attraction

1982 ◽  
Vol 32 (3) ◽  
pp. 328-331 ◽  
Author(s):  
C. M. Goldie ◽  
E. Seneta
Keyword(s):  
Recent Work ◽  
Sufficient Condition ◽  
Necessary And Sufficient Condition ◽  
Domain Of Partial Attraction ◽  
Necessary And Sufficient

AbstractA new necessary and sufficient condition for a distribution of unbounded support to be in a domain of partial attraction is given. This relates the recent work of [5] and [6].

The Photographic Process as a Diatomic Reaction

1960 ◽  
Vol 13 (2) ◽  
pp. 419 ◽  
Author(s):  
C Candler
Keyword(s):  
Trapped Electrons ◽  
Poisson Law ◽  
Sensitive Areas ◽  
Development Centre

If sensitive areas exist in unexposed crystals, the number of grains which develop on exposure is given by the Poisson law, and this conflicts with experiment; but, if a development centre is formed in a diatomic reaction triggered by P trapped electrons, the fraction n of the grains capable of development after an exposure E is

Limit Poisson law for the distribution of the number of components in generalized allocation scheme

2019 ◽  
Vol 29 (4) ◽  
pp. 255-266 ◽  
Author(s):  
Aleksandr N. Timashev
Keyword(s):  
Sufficient Conditions ◽  
Rooted Trees ◽  
Allocation Scheme ◽  
Number Of Components ◽  
Poisson Law ◽  
Generalized Allocation Scheme

Abstract We consider problems on the convergence of distributions of the total number of components and numbers of components with given volume to the Poisson law. Sufficient conditions of such convergence are given. Our results generalize known statemets on the limit Poisson laws of the number of components (cycles, unrooted and rooted trees, blocks and other structures) in the corresponding generalized of allocation schemes.

PATHS IN THE SIMPLE RANDOM GRAPH AND THE WAXMAN GRAPH

2001 ◽  
Vol 15 (4) ◽  
pp. 535-555 ◽  
Author(s):  
Piet Van Mieghem
Keyword(s):  
Probability Distribution ◽  
Random Graph ◽  
Higher Order ◽  
Higher Order Moments ◽  
Communications Networks ◽  
Poisson Law ◽  
Link Density

The Waxman graphs are frequently chosen in simulations as topologies resembling communications networks. For the Waxman graphs, we present analytic, exact expressions for the link density (average number of links) and the average number of paths between two nodes. These results show the similarity of Waxman graphs to the simpler class G>p(N). The first result enables one to compare simulations performed on the Waxman graph with those on other graphs with same link density. The average number of paths in Waxman graphs can be useful to dimension (or estimate) routing paths in networks. Although higher-order moments of the number of paths in Gp(N) are difficult to compute analytically, the probability distribution of the hopcount of a path between two arbitrary nodes seems well approximated by a Poisson law.

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