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Improved Chebyshev inequality: new probability bounds with known supremum of PDF [PDF]

open access: yesarXiv, 2018
In this paper, we derive new probability bounds for Chebyshev's inequality if the supremum of the probability density function is known. This result holds for one-dimensional or multivariate continuous probability distributions with finite mean and variance (covariance matrix).
arxiv  

On a distribution in frequency probability theory corresponding to the Bose-Einstein distribution [PDF]

open access: yesarXiv, 2006
The notion of density of a finite set is discussed. We proof a general theorem of set theory which refines Bose-Einstein distribution.
arxiv  

Extreme Points of the Convex Set of Joint Probability Distributions with Fixed Marginals [PDF]

open access: yesarXiv, 2007
By using a quantum probabilistic approach we obtain a description of the extreme points of the convex set of all joint probability distributions on the product of two standard Borel spaces with fixed marginal distributions.
arxiv  

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