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On the compound α(t)-modified Poisson distribution

Katarzyna SteligaDominik 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 random split of the segment

Milena BieniekDominik Szynal — 2005

Applicationes Mathematicae

We consider a partition of the interval [0,1] by two partition procedures. In the first a chosen piece of [0,1] is split into halves, in the second it is split by uniformly distributed points. Initially, the interval [0,1] is divided either into halves or by a uniformly distributed random variable. Next a piece to be split is chosen either with probability equal to its length or each piece is chosen with equal probability, and then the chosen piece is split by one of the above procedures. These...

On formulae for central moments of counting distributions

Katarzyna SteligaDominik 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.

On the Bayes estimators of the parameters of inflated modified power series distributions

Małgorzata MuratDominik Szynal — 2000

Discussiones Mathematicae Probability and Statistics

In this paper, we study the class of inflated modified power series distributions (IMPSD) where inflation occurs at any of support points. This class includes among others the generalized Poisson,the generalized negative binomial and the lost games distributions. We derive the Bayes estimators of parameters for these distributions when a parameter of inflation is known. First, we take as the prior distribution the uniform, Beta and Gamma distribution. In the second part of this paper, the prior...

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