We define a multivariate negative binomial distribution (MVNB) as a bivariate Poisson distribution function mixed with a multivariate exponential (MVE) distribution. We focus on the class of MVNB distributions generated by Marshall-Olkin MVE distributions. For simplicity of notation we analyze in detail the class of bivariate (BVNB) distributions. In applications the standard data from [2] and [7] and data concerning parasites of birds from [4] are used.
We assume that the result of a football game depends upon the difference of the strengths of the teams, home-field advantage, random factors and also other components. We describe the goal outcome per game by independent Poisson random variables; we concentrate on expected values. The least squares estimators of the parameters are obtained. The study is illustrated by examples from the Italian and Polish leagues.
The success-run in a sequence of Bernoulli trials was considered in a large number of papers. W. Feller [4] concentrates his attention on the number of runs what find the principal application in the theory of test of randomness and tests of homogeneity. Many papers deal with random variable Zn introduced by Erdos and Renyi [2] (see also Erdos and Revesz [3]), defined as the length of longest head-run during n coin tossings. They give the asymptotic estimations of that random variable if n tends...
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In the memoirs of Professor Hugo Steinhaus the problem of estimation of the war casualties of German Army during the SecondWorldWar on the base of contemporary press obituaries is mentioned.A ssuming the inflated geometric probability distribution function for the size of German family, introducing some transformations of this random variable and taking into account the probability distribution function of the contens of obituaries we propose in the note a solution of the problem.
The paper is devoted to the comparison of two preventive replacement strategies anticipating failures of working elements: a cyclic one and one based on the age of the elements. Several classes of reliability functions are considered for which these strategies are shown to be more or less efficient.
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