On conditions for the strong law of large numbers in general Banach spaces.
On complete convergence for randomly indexed sums for a case without identical distributions.
On complete convergence in a Banach space.
La convergence en probabilité et la convergence presque sûre de certaines suites de variables aléatoires dépendantes
Goodness-of-fit tests derived from characterizations of continuous distributions
Starting from characterizations of continuous distributions in terms of the expected values of two functions of record values we construct a family of goodness-of-fit tests calculated from U-statistics.
Review: Dobiesław Bobrowski; Probabilistic in technical applications
The article contains no abstract
On two families of tests for normality with empirical description of their performances
We discuss two families of tests for normality based on characterizations of continuous distributions via order statistics and record values. Simulations of their powers show that they are competitive to widely recommended tests in the literature.
Characterizations of the inverse Weibull distribution and generalized extreme value distributions by moments of kth record values
We give characterization conditions for the inverse Weibull distribution and generalized extreme value distributions by moments of kth record values.
Characterizations of uniform and exponential distributions via moments of the kth record values randomly indexed
We characterize uniform and exponential distributions via moments of the kth record statistics. Too and Lin's (1989) results are contained in our approach.
On functional measures of skewness
We introduce a concept of functional measures of skewness which can be used in a wider context than some classical measures of asymmetry. The Hotelling and Solomons theorem is generalized.
On monotone dependence functions of the quantile type
We introduce the concept of monotone dependence function of bivariate distributions without moment conditions. Our concept gives, among other things, a characterization of independent and positively (negatively) quadrant dependent random variables.
Characterizations of distributions by moments of order statistics when the sample size is random
We give characterizations of the uniform distribution in terms of moments of order statistics when the sample size is random. Special cases of a random sample size (logarithmic series, geometrical, binomial, negative binomial, and Poisson distribution) are also considered.
Goodness-of-fit tests based on characterizations of continuous distributions
We construct goodness-of-fit tests for continuous distributions using their characterizations in terms of moments of order statistics and moments of record values. Our approach is based on characterizations presented in [2]-[4], [5], [9].
On existence and an asymptotic behavior of random solutions of a class of stochastic functional-integral equations
On the compound α(t)-modified Poisson distribution
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
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...
Goodness-of-fit tests using characterizations of continuous distributions
Using characterization conditions of continuous distributions in terms of moments of order statistics and moments of record values we present new goodness-of-fit techniques.
On formulae for central moments of counting distributions
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
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...
Recurrence relations for single and product moments of k-th lower record values from the inverse distributions of Pareto's type and characterizations
We give recurrence relations for single and product moments of k-th lower record values from the inverse Pareto, inverse generalized Pareto and inverse Burr distributions. We present also characterization conditions for these distributions.
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