This paper derives characterizations of bivariate binomial distributions of the Lancaster form with Krawtchouk polynomial eigenfunctions. These have been characterized by Eagleson, and we give two further characterizations with a more probabilistic flavour: the first as sums of correlated Bernoulli variables; and the second as the joint distribution of the number of balls of one colour at consecutive time points in a generalized Ehrenfest urn. We give a self-contained development of Krawtchouck polynomials and Eagleson's theorem. © 2012 Australian Statistical Publishing Association Inc
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We study the degree distribution of the greatest common divisor of two or more random polynomials ov...
This paper is concerned with the exact joint tail distributions of order statistics for i.i.d. rando...
We present here a probabilistic approach to the generation of new polynomials in two discrete variab...
The quest continues for cases of interest where the differential equations for the Pólya process are...
A multivariable biorthogonal generalization of the Meixner, Krawtchouk, and Meixner–Pollaczek polyno...
This paper introduces a bivariate Dirichlet process for modelling a partially exchangeable sequence ...
This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distributi...
This paper defines the multivariate Krawtchouk polynomials, orthogonal on the multinomial distributi...
This paper introduces a bivariate Dirichlet process for modelling a partially exchangeable sequence ...
The thesis deals with three selected constructions of bivariate distributions. The first approach is...
AbstractThis paper presents a systematic introduction to and several applications of a certain metho...
AbstractA family of soluble Markov chains is introduced, which derive from simple prescriptions allo...
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Abstract. The study of sums of possibly associated Bernoulli random variables has been hampered by a...
AbstractMultivariate but vectorized versions for Bernoulli and binomial distributions are establishe...
We study the degree distribution of the greatest common divisor of two or more random polynomials ov...
This paper is concerned with the exact joint tail distributions of order statistics for i.i.d. rando...
We present here a probabilistic approach to the generation of new polynomials in two discrete variab...