Daly, Fraser Compound geometric approximation under a failure rate constraint. (English) Zbl 1351.62060 J. Appl. Probab. 53, No. 3, 700-714 (2016). Summary: We consider compound geometric approximation for a nonnegative, integer-valued random variable \(W\). The bound we give is straightforward but relies on having a lower bound on the failure rate of \(W\). Applications are presented to M/G/1 queuing systems, for which we state explicit bounds in approximations for the number of customers in the system and the number of customers served during a busy period. Other applications are given to birth-death processes and Poisson processes. Cited in 6 Documents MSC: 62E17 Approximations to statistical distributions (nonasymptotic) 60E15 Inequalities; stochastic orderings 60J10 Markov chains (discrete-time Markov processes on discrete state spaces) 62E10 Characterization and structure theory of statistical distributions Keywords:compound geometric distribution; failure rate; hazard rate ordering; M/G/1 queue; birth-death process; Poisson process × Cite Format Result Cite Review PDF Full Text: DOI arXiv