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On a problem by Schweizer and Sklar

Fabrizio Durante (2012)

Kybernetika

We give a representation of the class of all n -dimensional copulas such that, for a fixed m , 2 m < n , all their m -dimensional margins are equal to the independence copula. Such an investigation originated from an open problem posed by Schweizer and Sklar.

On a trivariate Poisson distribution

Sotirios Loukas, Evgenia H. Papageorgiou (1991)

Applications of Mathematics

A four parameter trivariate Poisson distribution is considered. Recurrences for the probabilities and the partial derivatives of the probabilities with respect to the parameters are derived. Solutions of the maximum likelihood equations are obtaired and the determinant of their asymptotic covariance matrix is given. Applications of the maximum likelihood estimation technique to simulated data sets are also examined.

On an inequality and the related characterization of the gamma distribution

Maia Koicheva (1993)

Applications of Mathematics

In this paper we derive conditions upon the nonnegative random variable under which the inequality D g ( ξ ) c E g ' ξ 2 ξ holds for a fixed nonnegative constant c and for any absolutely continuous function g . Taking into account the characterization of a Gamma distribution we consider the functional U ξ = sup g D g ξ E g ' ξ 2 ξ and establishing some of its properties we show that U ξ 1 and that U ξ = 1 iff the random variable ξ has a Gamma distribution.

On characteristic functions of kth record values from the generalized extreme value distribution and its characterization

M. A. W. Mahmoud, M. A. Atallah, M. Albassam (2011)

Applicationes Mathematicae

Recurrence relations for the marginal, joint and conditional characteristic functions of kth record values from the generalized extreme value distribution are established. These relations are utilized to obtain recurrence relations for single, product and conditional moments of kth record values. Moreover, by making use of the recurrence relations the generalized extreme value distribution is characterized.

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