Bounds for the characteristic functions of the system of monomials in random variables and of its trigonometric analogue.
Bounds for the Difference Between Median and Mean of Beta and Negative Binomial Distributions.
Bounds of general Fréchet classes
This paper deals with conditions of compatibility of a system of copulas and with bounds of general Fréchet classes. Algebraic search for the bounds is interpreted as a solution to a linear system of Diophantine equations. Classical analytical specification of the bounds is described.
Bounds on expectations of record range and record increment from distributions with bounded support.
Bounds on margin distributions in learning problems
Bounds on tail probabilities for negative binomial distributions
In this paper we derive various bounds on tail probabilities of distributions for which the generated exponential family has a linear or quadratic variance function. The main result is an inequality relating the signed log-likelihood of a negative binomial distribution with the signed log-likelihood of a Gamma distribution. This bound leads to a new bound on the signed log-likelihood of a binomial distribution compared with a Poisson distribution that can be used to prove an intersection property...
Bounds on the expectations of th record increments.
Burkholder's inequality for multiindex martingales.