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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.

On Dwass' method for deriving the distribution of rank order statistics

B. R. Handa, Sri Gopal Mohanty (1979)

Aplikace matematiky

This note presents a critical examination of Dwass' method for obtaining the distribution of rank order statistics defined on random samples obtained from the same continuous population. New situations are discussed for the usefulness of the method.

On fine properties of mixtures with respect to concentration of measure and Sobolev type inequalities

Djalil Chafaï, Florent Malrieu (2010)

Annales de l'I.H.P. Probabilités et statistiques

Mixtures are convex combinations of laws. Despite this simple definition, a mixture can be far more subtle than its mixed components. For instance, mixing gaussian laws may produce a potential with multiple deep wells. We study in the present work fine properties of mixtures with respect to concentration of measure and Sobolev type functional inequalities. We provide sharp Laplace bounds for Lipschitz functions in the case of generic mixtures, involving a transportation cost diameter of the mixed...

On formulae for central moments of counting distributions

Katarzyna Steliga, Dominik 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 functional measures of skewness

Renata Dziubińska, Dominik Szynal (1996)

Applicationes Mathematicae

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.

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