A Characteristic Property for Maxima of Random Variables with Trivial Analogue When Sums are Concerned
A characterization of the set of fixed points of the quicksort transformation.
A discrete time queueing system with departures having random memory
A Distribution of Class L Arising in the Theory of Risk
A factorisation of the Askey’s characteristic function
A generalized beta function and associated probability density.
A method constructing density functions: the case of a generalized Rayleigh variable
In this paper we propose a new generalized Rayleigh distribution different from that introduced in Apl. Mat. 47 (1976), pp. 395–412. The construction makes use of the so-called “conservability approach” (see Kybernetika 25 (1989), pp. 209–215) namely, if is a positive continuous random variable with a finite mean-value , then a new density is set to be , where is the probability density function of . The new generalized Rayleigh variable is obtained using a generalized form of the exponential...
A new characterization of geometric distribution
A characterization of geometric distribution is given, which is based on the ratio of the real and imaginary part of the characteristic function.
A note on Pólya's theorem.
The class of extended Pólya functions Ω = {φ: φ is a continuous real valued real function, φ(-t) = φ(t) ≤ φ(0) ∈ [0,1], límt→∞ φ(t) = c ∈ [0,1] and φ(|t|) is convex} is a convex set. Its extreme points are identified, and using Choquet's theorem it is shown that φ ∈ Ω has an integral representation of the form φ(|t|) = ∫0∞ max{0, 1-|t|y} dG(y), where G is the distribution function of some random variable Y. As on the other hand max{0, 1-|t|y} is the characteristic function of an absolutely continuous...
A note on probabilistic representations of operator semigroups.
A numerical constant associated with generalized convolutions
Time Series with Approximated Beta Marginal
A representation of the characteristic functions of stable distributions in Hilbert spaces
A simple proof of Fishburn's moments theorem.
We derive a necessary condition for stochastic dominance of any order based on the Laplace transform of probability measures on [0,∞) for which it follows easily Fishburn's theorem on the lexicographic order of the moments.
A stochastic fixed point equation related to weighted branching with deterministic weights.
A Stochastic Multiplicative Model in Assessment of Training Programs
A strong limit theorem for functions of continuous random variables and an extension of the Shannon-McMillan theorem.
A theoretical argument why the -copula explains credit risk contagion better than the Gaussian copula.
About the density of spectral measure of the two-dimensional SaS random vector
In this paper, we consider a symmetric α-stable p-sub-stable two-dimensional random vector. Our purpose is to show when the function is a characteristic function of such a vector for some p and α. The solution of this problem we can find in [3], in the language of isometric embeddings of Banach spaces. Our proof is based on simple properties of stable distributions and some characterization given in [4].
About the generating function of a left bounded integer-valued random variable
We give a relation between the sign of the mean of an integer-valued, left bounded, random variable and the number of zeros of inside the unit disk, where is the generating function of , under some mild conditions