This paper explores characterizations of Bivariate Binomial distributions of the Lancaster form with Krawtchouk polynomial eigenfunctions which are equivalent to a characterization by Eagleson (1969). Generalized Ehrenfest urns with Binomial stationary distributions have transition functions which are equivalent to the Lancaster distributions. There is a partial extension to d-colour ball Ehren...

Diierent universal (also called automatic or black-box) methods have been suggested to sample from univariate log-concave distributions. The description of a universal generator for bivariate distributions has not been published up to now. The new algorithm for bivariate log-concave distributions is based on the method of transformed density rejection. In order to construct a hat function for a...

The correlation among multiple lines of business plays a critical role in aggregating claims and thus determining loss reserves for an insurance portfolio. We show that the Sarmanov family of bivariate distributions is a convenient choice to capture the dependencies introduced by various sources, including the common calendar year, accident year and development period effects. The density of th...

We prove a two-dimensional version of the famous Pickands–Balkema–de Haan theorem of extreme value theory. The bivariate random variables are generated using the copula language. This representation of dependence structures allows to derive asymptotic results for bivariate excess distributions.  2003 Elsevier SAS. All rights reserved. Résumé Une version en dimension 2 du célèbre théorème de Pi...

Universal constructions of univariate and bivariate Gaussian distributions, as transformations of diffuse probability distributions via, respectively, planeand space-filling fractal interpolating functions and the central limit theorems that they imply, are reviewed. It is illustrated that the construction of the bivariate Gaussian distribution yields exotic kaleidoscopic decompositions of the ...

An extension of FGM class of bivariate distributions with given marginals is presented. For Huang-Kotz FGM distributions some theorems characterizing symmetry and conditions for independence are obtained. The new family of distributions allows us to achieve correlation between the components greater than 0.5.

In this paper we discuss the problem on parametric and non parametric estimation of the distributions generated by the Marshall-Olkin copula. This copula comes from the Marshall-Olkin bivariate exponential distribution used in reliability analysis. Through this copula we can extend the Marshall-Olkin distribution in order to construct several bivariate survival functions. The cumulative distrib...

A catalogue record for this book is available from the British Library Library of Congress Cataloguing in Publication data Spanos, Aris, 1952– Probability Theory and Statistical Inference: econometric modeling with observational data / Aris Spanos p. cm. Includes bibliographical references (p.) and index. Contents Preface page xi Acknowledgments xxiv 1 An introduction to empirical modeling 1 1....

In this paper, we introduce a new skewed distribution of which normal and power normal distributions are two special cases. This distribution is obtained by taking geometric maximum of independent identically distributed power normal random variables. We call this distribution as the power normal--geometric distribution. Some mathematical properties of the new distribution are presented. Maximu...