### La convergence en probabilité et la convergence presque sûre de certaines suites de variables aléatoires dépendantes

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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.

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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.

We give characterization conditions for the inverse Weibull distribution and generalized extreme value distributions by moments of kth record values.

We characterize uniform and exponential distributions via moments of the kth record statistics. Too and Lin's (1989) results are contained in our approach.

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.

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.

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.

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].

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.

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...

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.

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.

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...

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.

The paper is concerned with a problem of optimal linear filtering in the case where exists correlation between the noises w(k) of the plant and noises v(k) and v(k+1) of the meter. The algorithm obtained contains the classical Kalman's solution and its generalization given by Simkin [5]. The dual problem under these conditions is also considered.

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