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On the compound α(t)-modified Poisson distribution

Katarzyna Steliga;  Dominik Szynal — 2015

Applicationes Mathematicae

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.

On formulae for central moments of counting distributions

Katarzyna Steliga;  Dominik Szynal — 2015

Applicationes Mathematicae

The aim of this article is to give new formulae for central moments of the binomial, negative binomial, Poisson and logarithmic distributions. We show that they can also be derived from the known recurrence formulae for those moments. Central moments for distributions of the Panjer class are also studied. We expect our formulae to be useful in many applications.

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