Ramdom variables related to distributions of sums modulo an integer.
Random Integrals and Type and Cotype of Banach Space.
Random mappings, forests, and subsets associated with Abel-Cayley-Hurwitz multinomial expansions.
Random noise and perturbation of copulas
For a random vector characterized by a copula we study its perturbation characterizing the random vector affected by a noise independent of both and . Several examples are added, including a new comprehensive parametric copula family .
Random Sum Representation Of The Noncentral Chi-Square Random Variable.
Random Sums Of Random Vectors
Random variables, joint distribution functions, and copulas
Random walk over a hypersphere.
Rare events and conditional events on random strings.
Ratio of the tail of an infinitely divisible distribution on the line to that of its Lev́y measure.
Réarrangement, inégalités maximales et théorèmes ergodiques fractionnaires
Étant donné un semi-flot mesurable préservant une mesure de probabilité sur un espace , nous considérons les moyennes ergodiques où est un “poids” à support compact sur , c’est-à-dire que vérifie et . Nous démontrons la convergence p.p. de ces moyennes quand si appartient à l’espace de Lorentz défini par le poids qui est le réarrangé décroissant de . En particulier, pour , on obtient la convergence p.p. des moyennes de Césarò d’ordre
Recurrence relations for single and product moments of k-th lower record values from the inverse distributions of Pareto's type and characterizations
We give recurrence relations for single and product moments of k-th lower record values from the inverse Pareto, inverse generalized Pareto and inverse Burr distributions. We present also characterization conditions for these distributions.
Recurring mean inequality of random variables.
Refinements of inequalities between the sum of squares and the exponential of sum of a nonnegative sequence.
Rekursionsformeln für die zentralen Momente der PÖLYA- und der Beta-Verteilung.
Relations for characteristic functions of k-th record values from generalized Pareto and inverse generalized Pareto distribution
Relations for the marginal, joint, conditional characteristic functions of k-th upper and lower record values from generalized Pareto distribution and inverse generalized Pareto distribution are given.
Relationship between stochastic inequalities and some classical mathematical inequalities.
Relative entropy and stability of stochastic semigroups
Remark on Polya's law
Remarks on Catalan and super-Catalan numbers
In this article we discuss the Catalan and super-Catalan (or Schröder) numbers. We start with some combinatorial interpretations of those numbers. We study two probability measures in the context of free probability, one whose moments are super-Catalan, and another, whose even moments are super-Catalan and odd moments are zero. With the use of the latter we also show some new formulae for evaluation of the Catalans in terms of super-Catalans and vice-versa.