Exercise Manual in Probability theory - J. Stoyanov, I. Mirazchiiski, Z. Ignatov and M. Tanushev.
On a bivariate Poisson-geometric distribution
Recursive formulas for aggregate claim distributions
On Bivariate Generalized Binomial and Negative Binomial Distributions.
Existence of solutions and of multiple solutions for nonlinear nonsmooth periodic systems
In this paper we examine nonlinear periodic systems driven by the vectorial -Laplacian and with a nondifferentiable, locally Lipschitz nonlinearity. Our approach is based on the nonsmooth critical point theory and uses the subdifferential theory for locally Lipschitz functions. We prove existence and multiplicity results for the “sublinear” problem. For the semilinear problem (i.e. ) using a nonsmooth multidimensional version of the Ambrosetti-Rabinowitz condition, we prove an existence theorem...
On a trivariate Poisson distribution
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.
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