A note on new classes of infinitely divisible distributions on .
A note on optimal probability lower bounds for centered random variables
We obtain lower bounds for ℙ(ξ ≥ 0) and ℙ(ξ > 0) under assumptions on the moments of a centered random variable ξ. The estimates obtained are shown to be optimal and improve results from the literature. They are then applied to obtain probability lower bounds for second order Rademacher chaos.
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 note on probability weighted moment inequalities for reliability measures.
A note on stability of multivariate distributions.
In this note we give an elementary proof of a characterization for stability of multivariate distributions by considering a functional equation.
A note on stochastic ordering of estimators of exponential reliability
Recently Balakrishnan and Iliopoulos [Ann. Inst. Statist. Math. 61 (2009)] gave sufficient conditions under which the maximum likelihood estimator (MLE) is stochastically increasing. In this paper we study test plans which are not considered there and we prove that the MLEs for those plans are also stochastically ordered. We also give some applications to the estimation of reliability.
A note on sums of independent uniformly distributed random variables
A note on Talagrand's concentration inequality.
A note on the distributions of the maximum of linear Bernoulli processes.
A note on the Ehrhard inequality
We prove that for λ ∈ [0,1] and A, B two Borel sets in with A convex, , where is the canonical gaussian measure in and is the inverse of the gaussian distribution function.
A note on the functional law of the iterated logarithm for Lévy's area process
By using large deviation techniques, we prove a Strassen type law of the iterated logarithm, in Hölder norm, for Lévy's area process.
A note on the good lambda inequalities
A note on the interval-valued marginal problem and its maximum entropy solution
This contribution introduces the marginal problem, where marginals are not given precisely, but belong to some convex sets given by systems of intervals. Conditions, under which the maximum entropy solution of this problem can be obtained via classical methods using maximum entropy representatives of these convex sets, are presented. Two counterexamples illustrate the fact, that this property is not generally satisfied. Some ideas of an alternative approach are presented at the end of the paper.
A note on the martingale inequality.
A Note on the Men'shov-Rademacher Inequality
We improve the constants in the Men’shov-Rademacher inequality by showing that for n ≥ 64, for all orthogonal random variables X₁,..., Xₙ such that .
A note on the tail accuracy of the univariate saddlepoint approximation
A note on the upper bounds for the dispersion.
A numerical constant associated with generalized convolutions
A probabilistic proof of the series representation of the Macdonald function with applications.