Bounds for the characteristic functions of the system of monomials in random variables and of its trigonometric analogue.
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Shervashidze, T. (1997)
Georgian Mathematical Journal
J.H. Young, M.E. Payton, L.J. Young (1989)
Metrika
Jaroslav Skřivánek (2012)
Kybernetika
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.
Raqab, Mohammad Z. (2007)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Vladimir Koltchinskii (2003)
Annales de l'I.H.P. Probabilités et statistiques
Peter Harremoës (2016)
Kybernetika
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...
Raqab, Mohammad Z. (2004)
JIPAM. Journal of Inequalities in Pure & Applied Mathematics [electronic only]
Fazekas, István (2005)
Annales Mathematicae et Informaticae
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