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On Mieshalkin-Rogozin theorem and some properties of the second kind beta distribution

Włodzimierz Krysicki (2000)

Discussiones Mathematicae Probability and Statistics

The decomposition of the r.v. X with the beta second kind distribution in the form of finite (formula (9), Theorem 1) and infinity products (formula (17), Theorem 2 and form (21), Theorem 3) are presented. Next applying Mieshalkin - Rogozin theorem we receive the estimation of the difference of two c.d.f. F(x) and G(x) when sup|f(t) - g(t)| is known, improving the result of Gnedenko - Kolmogorov (formulae (23) and (24)).

On quasi-homogeneous copulas

Gaspar Mayor, Radko Mesiar, Joan Torrens (2008)

Kybernetika

Quasi-homogeneity of copulas is introduced and studied. Quasi-homogeneous copulas are characterized by the convexity and strict monotonicity of their diagonal sections. As a by-product, a new construction method for copulas when only their diagonal section is known is given.

On small sample inference for common mean in heteroscedastic one-way model

Viktor Witkovský, Alexander Savin, Gejza Wimmer (2003)

Discussiones Mathematicae Probability and Statistics

In this paper we consider and compare several approximate methods for making small-sample statistical inference on the common mean in the heteroscedastic one-way random effects model. The topic of the paper was motivated by the problem of interlaboratory comparisons and is also known as the (traditional) common mean problem. It is also closely related to the problem of multicenter clinical trials and meta-analysis. Based on our simulation study we suggest to use the approach proposed by Kenward...

On some Mixture Distributions

Nakhi, Y. Ben, Kalla, S.L. (2004)

Fractional Calculus and Applied Analysis

The aim of this paper is to establish some mixture distributions that arise in stochastic processes. Some basic functions associated with the probability mass function of the mixture distributions, such as k-th moments, characteristic function and factorial moments are computed. Further we obtain a three-term recurrence relation for each established mixture distribution.

On the asymptotic efficiency of the multisample location-scale rank tests and their adjustment for ties

František Rublík (2007)

Kybernetika

Explicit formulas for the non-centrality parameters of the limiting chi-square distribution of proposed multisample rank based test statistics, aimed at testing the hypothesis of the simultaneous equality of location and scale parameters of underlying populations, are obtained by means of a general assertion concerning the location-scale test statistics. The finite sample behaviour of the proposed tests is discussed and illustrated by simulation estimates of the rejection probabilities. A modification...

On the asymptotic properties of rank statistics for the two-sample location and scale problem

Mohamed N. Goria, Dana Vorlíčková (1985)

Aplikace matematiky

The equivalence of the symmetry of density of the distribution of observations and the oddness and evenness of the score-generating functions for the location and the scale problem, respectively, is established at first. Then, it is shown that the linear rank statistics with scores generated by these functions are asymptotically independent under the hypothesis of randomness as well as under contiguous alternatives in the last part of the paper. The linear and quadratic forms of these statistics...

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

Małgorzata Murat, Dominik 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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