Results 21 to 30 of about 138 (124)

Moment inequalities connected with accompanying Poisson laws in Abelian groups

International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 44, Page 2771-2786, 2003., 2003
We obtain exact inequalities which connect moments of some functions of sums of independent random variables taking values in a measurable Abelian group and those for the accompanying infinitely divisible laws. Some applications to empirical processes are studied.
I. S. Borisov
wiley   +1 more source

Dependence uncertainty bounds for the energy score and the multivariate Gini mean difference

Dependence Modeling, 2020
The energy distance and energy scores became important tools in multivariate statistics and multivariate probabilistic forecasting in recent years. They are both based on the expected distance of two independent samples. In this paper we study dependence
Bernard Carole, Müller Alfred
doaj   +1 more source

Stochastic orders for a multivariate Pareto distribution

Analele Stiintifice ale Universitatii Ovidius Constanta: Seria Matematica, 2021
In this article we give some theoretical results for equivalence between different stochastic orders of some kind multivariate Pareto distribution family.
Catana Luigi-Ionut
doaj   +1 more source

Complete convergence for negatively dependent random variables

International Journal of Stochastic Analysis, Volume 16, Issue 2, Page 121-126, 2003., 2003
In this paper, we study the complete convergence for the means 1n∑i=1nXi and 1nα∑k=1nXnk via. exponential bounds, where α > 0 and {Xn, n ≥ 1} is a sequence of negatively dependent random variables and {Xnk, 1 ≤ k ≤ n, n ≥ 1} is an array of rowwise pairwise negatively dependent random variables.
M. Amini D., A. Bozorgnia
wiley   +1 more source

New continuity estimates of geometric sums

International Journal of Stochastic Analysis, Volume 15, Issue 3, Page 219-233, 2002., 2002
The paper deals with sums of a random number of independent and identically distributed random variables. More specifically, we compare two such sums, which differ from each other in the distributions of their summands. New upper bounds (inequalities) for the uniform distance between distributions of sums are established.
Evgueni Gordienko, Juan Ruiz de Chávez
wiley   +1 more source

Stochastic comparisons and bounds for conditional distributions by using copula properties

Dependence Modeling, 2018
We prove that different conditional distributions can be represented as distorted distributions. These representations are used to obtain stochastic comparisons and bounds for them based on properties of the underlying copula.
Navarro Jorge, Sordo Miguel A.
doaj   +1 more source

Negatively dependent bounded random variable probability inequalities and the strong law of large numbers

International Journal of Stochastic Analysis, Volume 13, Issue 3, Page 261-267, 2000., 2000
Let X1, …, Xn be negatively dependent uniformly bounded random variables with d.f. F(x). In this paper we obtain bounds for the probabilities P(|∑i=1nXi|≥nt) and P(|ξˆpn−ξp|>ϵ) where ξˆpn is the sample pth quantile and ξp is the pth quantile of F(x). Moreover, we show that ξˆpn is a strongly consistent estimator of ξp under mild restrictions on F(x) in
M. Amini, A. Bozorgnia
wiley   +1 more source

Bounds for distribution functions of sums of squares and radial errors

International Journal of Mathematics and Mathematical Sciences, Volume 14, Issue 3, Page 561-569, 1991., 1991
Bounds are found for the distribution function of the sum of squares X2 + Y2 where X and Y are arbitrary continuous random variables. The techniques employed, which utilize copulas and their properties, show that the bounds are pointwise best‐possible when X and Y are symmetric about 0 and yield expressions which can be evaluated explicitly when X and ...
Roger B. Nelsen, Berthold Schweizer
wiley   +1 more source

Worst case portfolio vectors and diversification effects

, 2010
Dependent risks, Risk bounds, Diversification, Comonotone vectors, 60E15, 91B30, G32, C43,
Ludger Rüschendorf
core   +1 more source

Inequalities for Walsh like random variables

International Journal of Mathematics and Mathematical Sciences, Volume 13, Issue 2, Page 353-356, 1990., 1990
Let be a sequence of mean zero independent random variables. Let , and let [Yk] be the linear span of Yk. Assume δ ≤ |Xn| ≤ K for some δ > 0 and K > 0 and let for 1 < p < ∞. We show that for f ∈ [Ym] the following inequalities hold: and ‖f‖2 ≤ C(4,m)2‖f‖1 ≤ C(4,m)2‖f‖2. These generalize various well known inequalities on Walsh functions.
D. Hajela
wiley   +1 more source