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On the distance between convex-ordered random variables, with applications

Part of: Limit theorems Distribution theory - Probability Distribution theory

Published online by Cambridge University Press:  01 July 2016

Michael V. Boutsikas  and
Eutichia Vaggelatou
Michael V. Boutsikas*
Affiliation:
University of Piraeus
Eutichia Vaggelatou*
Affiliation:
National Technical University of Athens
*
∗ Postal address: Department of Statistics and Insurance Science, University of Piraeus, 80 Karaoli and Dimitriou str., 185 34 Piraeus, Greece. Email address: [email protected]
∗∗ Postal address: Department of Applied Mathematics and Physical Sciences, National Technical University of Athens, GR-15780 Athens, Greece.
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Abstract

Simple approximation techniques are developed exploiting relationships between generalized convex orders and appropriate probability metrics. In particular, the distance between s-convex ordered random variables is investigated. Results connecting positive or negative dependence concepts and convex ordering are also presented. These results lead to approximations and bounds for the distributions of sums of positively or negatively dependent random variables. Applications and extensions of the main results pertaining to compound Poisson, normal and exponential approximation are provided as well.

Keywords

Stochastic orders of convex typeprobability metricspositive dependencenegative dependencecompound Poisson approximationrate of convergence in CLTexponential approximationgeometric convolutionsageing distributions

MSC classification

Primary: 60E15: Inequalities; stochastic orderings 62E17: Approximations to distributions (nonasymptotic)
Secondary: 60F05: Central limit and other weak theorems 62E20: Asymptotic distribution theory
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 34 , Issue 2 , June 2002 , pp. 349 - 374
Copyright
Copyright © Applied Probability Trust 2002 

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