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On smoothing properties of compound Poisson distributions
Lithuanian Mathematical Journal, 1995The main contributions are estimates of analogs of the uniform Kolmogorov distance and Lévy concentration function of products of terms of the type \((F-E)^k\exp[a(F-E)]\), where products and powers are in the convolution sense, \(F\) is a distribution function and \(E\) is the distribution concentrated at zero.
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An Estimate of the Compounding Distribution of a Compound Poisson Distribution
Theory of Probability & Its Applications, 1963The distribution of a random variable X is called a compound Poisson distribution if ${\bf P}\{ X = n\} = \int_0^\infty {\frac{{\lambda ^n }} {{n1}}} \varepsilon ^{ - \lambda } dG(\lambda ),$. where $n = 0,1,2, \cdots $ and $G(\lambda )$ is a distribution function (weight function) such that $G( + 0) = 0$.
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Characterizations of discrete compound Poisson distributions
Communications in Statistics - Theory and Methods, 2016ABSTRACTThe aim of this paper is to give some new characterizations of discrete compound Poisson distributions. Firstly, we give a characterization by the Levy–Khintchine formula of infinitely divisible distributions under some conditions. The second characterization need to present by row sum of random triangular arrays converges in distribution.
Huiming Zhang, Bo Li
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On the compound $\alpha (t)$-modified Poisson distribution
Applicationes Mathematicae, 2016Summary: In this paper we introduce compound \(\alpha (t)\)-modified Poisson distributions. We obtain the compound Delaporte distribution as the special case of the compound \(\alpha (t)\)-modified Poisson distribution. The characteristics of \(\alpha (t)\)-modified Poisson and some compound distributions with gamma, exponential and Panjer summands are
Steliga, Katarzyna, Szynal, Dominik
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Spatial Event Cluster Detection Using a Compound Poisson Distribution
Biometrics, 2006Summary Geographic disease surveillance methods identify regions that have higher disease rates than expected. These approaches are generally applied to incident or prevalent cases of disease. In some contexts, disease‐related events rather than individuals are the appropriate units of analysis for geographic surveillance. We propose a compound Poisson
Rhonda J, Rosychuk +2 more
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Approximation of aggregate claims distributions by compound poisson distributions
Insurance: Mathematics and Economics, 1985Error estimates are given for the approximation of the individual model of risk theory by compound Poisson distributions. Theoretical portfolios and one life portfolio from practice demonstrate the quality of the estimates.
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Moment Characteristics of the Compound Poisson Law Generalized by the Poisson Distribution
Computational Mathematics and Modeling, 2004The authors study a compound Poisson law generalized by a Poisson distribution. For the weighted sum \(\zeta = \zeta_1+2\zeta_2+\cdots +k\zeta_k\) of \(k\) independent Poisson random variables, they consider the conditional random variable \(\xi/\zeta\) following the Poisson distribution with parameter \(\epsilon\zeta ...
Belov, A. G., Galkin, V. Ya.
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A new compounding life distribution: the Weibull–Poisson distribution
Journal of Applied Statistics, 2012In this paper, a new compounding distribution, named the Weibull–Poisson distribution is introduced. The shape of failure rate function of the new compounding distribution is flexible, it can be decreasing, increasing, upside-down bathtub-shaped or unimodal.
Wanbo Lu, Daimin Shi
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Characterization of the Compound Poisson Distribution [PDF]
, 1979 Consider two non-negative integer-valued r.v.'s X,Y with X=>Y. Suppose that the conditional distribution of Y|X is binomial with parameters (n,p), n=0,1,2,...; 0 0 (Poisson(λp)) if and only if (iff) X is Poisson (λ). This model has been extensively used in the literature under different names in many practical situations.
Xekalaki, Evdokia, Panaretos, John
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