On the zeroes of some random functions
On Three and Five Parameter Bivariate Beta Distributions.
On two functional equations connected with the characterizations of the distance measures.
On uniform tail expansions of multivariate copulas and wide convergence of measures
The theory of copulas provides a useful tool for modeling dependence in risk management. In insurance and finance, as well as in other applications, dependence of extreme events is particularly important, hence there is a need for a detailed study of the tail behaviour of multivariate copulas. We investigate the class of copulas having regular tails with a uniform expansion. We present several equivalent characterizations of uniform tail expansions. Next, basing on them, we determine the class of...
Open problems posed at the tenth International conference on fuzzy set theory and applications (FSTA 2010, Liptovský Ján, Slovakia)
Eighteen open problems posed during FSTA 2010 (Liptovský Ján, Slovakia) are presented. These problems concern copulas, triangular norms and related aggregation functions. Some open problems concerning effect algebras are also included.
Operations on distribution functions not derivable from operations on random variables
Optimal nonlinear transformations of random variables
In this paper we deepen the study of the nonlinear principal components introduced by Salinelli in 1998, referring to a real random variable. New insights on their probabilistic and statistical meaning are given with some properties. An estimation procedure based on spline functions, adapting to a statistical framework the classical Rayleigh–Ritz method, is introduced. Asymptotic properties of the estimator are proved, providing an upper bound for the rate of convergence under suitable mild conditions....
Optimal two-value zero-mean disintegration of zero-mean random variables.
Order relations in the set of probability distribution functions and their applications in queueing theory [Book]
Plongement de lois indéfiniment divisibles
Plug-in estimation of level sets in a non-compact setting with applications in multivariate risk theory
This paper deals with the problem of estimating the level sets L(c) = {F(x) ≥ c}, with c ∈ (0,1), of an unknown distribution function F on ℝ+2. A plug-in approach is followed. That is, given a consistent estimator Fn of F, we estimate L(c) by Ln(c) = {Fn(x) ≥ c}. In our setting, non-compactness property is a priori required for the level sets to estimate. We state consistency results with respect to the Hausdorff distance and the volume of the symmetric difference. Our results are motivated by...
Poisson random sums of present Values of Continuous Uniform cash flows
Polynomial expansions of density of power mixtures
For any given random variable Y with infinitely divisible distribution in a quadratic natural exponential family we obtain a polynomial expansion of the power mixture density of Y. We approach the problem generally, and then consider certain distributions in greater detail. Various applications are indicated and the results are also applied to obtain approximations and their error bounds. Estimation of density and goodness-of-fit test are derived.
Principes d'invariance pour la probabilité d'un dilaté de l'enveloppe convexe d'un échantillon
Probabilistic derivation of a bilinear summation formula for the Meixner- Pollaczek polynomials.
Probabilistische Metriken auf der Menge der nicht negativen Verteilungsfunktion.
Probability distribution solutions of a general linear equation of infinite order
Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We obtain a partial characterization and a uniqueness-type result for solutions of the general linear equation in the class of probability distribution functions.
Probability distribution solutions of a general linear equation of infinite order, II
Let (Ω,,P) be a probability space and let τ: ℝ × Ω → ℝ be a mapping strictly increasing and continuous with respect to the first variable, and -measurable with respect to the second variable. We discuss the problem of existence of probability distribution solutions of the general linear equation . We extend our uniqueness-type theorems obtained in Ann. Polon. Math. 95 (2009), 103-114.
Product Bessel distributions of the first and second kinds.
Properties of matrix variate beta type 3 distribution.