Abstract
We consider the tail probabilities of a class of compound distributions. First, the relations between reliability distribution classes and heavy-tailed distributions are discussed. These relations reveal that many previous results on estimating the tail probabilities are not applicable to heavy-tailed distributions.Then, a generalized Wald's identity and identities for compound geometric distributions are presented in terms of renewal processes. Using these identities, lower and upper bounds for the tail probabilities are derived in a unified way for the class of compound distributions, both under the conditions of NBU and NWU tails, which include exponential tails, as well as under the condition of heavy-tailed distributions.Finally, simplified bounds are derived by the technique of stochastic ordering. This method removes some unnecessary technical assumptions and corrects errors in the proof of some previous results.
Publisher
Cambridge University Press (CUP)
Subject
Statistics, Probability and Uncertainty,General Mathematics,Statistics and Probability
Cited by
22 articles.
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