On the Exponential Law.
On the functional equation f(x) g(y) = p(x+y) q(x/y).
On the functional equation f(x) g(y) = p(x+y) q(x/y). (Short Communication).
On the generalization of the STER distribution applied to generalized hypergeometric parents
On the Heyde theorem for discrete Abelian groups
Let X be a countable discrete Abelian group, Aut(X) the set of automorphisms of X, and I(X) the set of idempotent distributions on X. Assume that α₁, α₂, β₁, β₂ ∈ Aut(X) satisfy . Let ξ₁, ξ₂ be independent random variables with values in X and distributions μ₁, μ₂. We prove that the symmetry of the conditional distribution of L₂ = β₁ξ₁ + β₂ξ₂ given L₁ = α₁ξ₁ + α₂ξ₂ implies that μ₁, μ₂ ∈ I(X) if and only if the group X contains no elements of order two. This theorem can be considered as an analogue...
On the Lukacs property for free random variables
The Lukacs property of the free Poisson distribution is studied. We prove that if free and are free Poisson distributed with suitable parameters, then + and are free. As an auxiliary result we compute the joint cumulants of and for free Poisson distributed . We also study the Lukacs property of the free Gamma distribution.
On the Property of Dullness of Pareto Distribution.
On the robustness of properties characterizing the normal distribution
On the significance level of the multirelation coefficient.
On the spectrum of a distribution function and on unique factorization.
Parameter estimation of sub-Gaussian stable distributions
In this paper, we present a parameter estimation method for sub-Gaussian stable distributions. Our algorithm has two phases: in the first phase, we calculate the average values of harmonic functions of observations and in the second phase, we conduct the main procedure of asymptotic maximum likelihood where those average values are used as inputs. This implies that the main procedure of our method does not depend on the sample size of observations. The main idea of our method lies in representing...
Performance of hedging strategies in interval models
For a proper assessment of risks associated with the trading of derivatives, the performance of hedging strategies should be evaluated not only in the context of the idealized model that has served as the basis of strategy development, but also in the context of other models. In this paper we consider the class of so-called interval models as a possible testing ground. In the context of such models the fair price of a derivative contract is not uniquely determined and we characterize the interval...
Polya tree distributions for statistical modeling of censored data.
Product Bessel distributions of the first and second kinds.
Propiedades de las funciones de medias de las distribuciones truncadas.
En este trabajo, utilizando el concepto de distribuciones truncadas obtenidas de una distribución unidimensional de función de distribución dada F(x), se introduce el de función de medias m(x), estudiándose sus propiedades. Se obtienen condiciones necesarias para que una función real dada pueda ser función de medias. Se plantea la conjetura de que las condiciones que se señalan sean también suficientes, así como el problema de dar forma explícita a la inversa de la transformación funcional que se...
Proving the characterization of Archimedean copulas via Dini derivatives
In this note we prove the characterization of the class of Archimedean copulas by using Dini derivatives.
Quelles fonctions changent toute loi uniforme en une loi uniforme ?
Record indices and age-ordered frequencies in exchangeable Gibbs partitions.
Records and concomitants.
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.