Estimation of interarrival time distribution from short time windows
Zbyněk Pawlas (2011)
Acta Universitatis Carolinae. Mathematica et Physica
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Zbyněk Pawlas (2011)
Acta Universitatis Carolinae. Mathematica et Physica
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Z. Schenková (1982)
Acta Universitatis Carolinae. Mathematica et Physica
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S Loukas (1991)
Applicationes Mathematicae
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Sotirios Loukas, Evgenia H. Papageorgiou (1991)
Applications of Mathematics
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A four parameter trivariate Poisson distribution is considered. Recurrences for the probabilities and the partial derivatives of the probabilities with respect to the parameters are derived. Solutions of the maximum likelihood equations are obtaired and the determinant of their asymptotic covariance matrix is given. Applications of the maximum likelihood estimation technique to simulated data sets are also examined.
Katarzyna Steliga, Dominik Szynal (2015)
Applicationes Mathematicae
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In this paper we introduce compound α(t)-modified Poisson distributions. We obtain the compound Delaporte distribution as the special case of the compound α(t)-modified Poisson distribution. The characteristics of α(t)-modified Poisson and some compound distributions with gamma, exponential and Panjer summands are presented.
Gnedin, Alexander (2008)
Electronic Communications in Probability [electronic only]
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M. Majsnerowska (1998)
Applicationes Mathematicae
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One more method of Poisson approximation is presented and illustrated with examples concerning binomial, negative binomial and hypergeometric distributions.
Raghavendra Krishna, Varahamurti (1967)
Portugaliae mathematica
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Aldona Aleškevičienė, Vytautas Statulevičius (2005)
Discussiones Mathematicae Probability and Statistics
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We present here the results of the investigation on approximation by the Poisson law of distributions of sums of random variables in the scheme of series. We give the results pertaining to the behaviour of large deviation probabilities and asymptotic expansions, to the method of cumulants, with the aid of which our results have been obtained.
Alice Cleynen, Emilie Lebarbier (2014)
ESAIM: Probability and Statistics
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We consider the segmentation problem of Poisson and negative binomial (overdispersed Poisson) rate distributions. In segmentation, an important issue remains the choice of the number of segments. To this end, we propose a penalized -likelihood estimator where the penalty function is constructed in a non-asymptotic context following the works of L. Birgé and P. Massart. The resulting estimator is proved to satisfy an oracle inequality. The performances of our criterion is assessed using...