On applications of residual lifetimes of compound geometric convolutions

DOI10.1239/jap/1091543427zbMath1092.62018OpenAlexW2070856327MaRDI QIDQ4668002

Jun Cal, Gordon E. Willmot

Publication date: 18 April 2005

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1091543427

zbMATH Keywords

queueing theoryrenewal risk modelcompound geometric distributionNBU/NWU and analogous properties

Mathematics Subject Classification ID

Queueing theory (aspects of probability theory) (60K25) Characterization and structure theory of statistical distributions (62E10) Reliability and life testing (62N05) Applications of queueing theory (congestion, allocation, storage, traffic, etc.) (60K30)

Related Items (8)

On the complete monotonicity of the compound geometric convolution with applications in risk theory ⋮ On the analysis of ruin-related quantities in the delayed renewal risk model ⋮ On the DFR property of the compound geometric distribution with applications in risk theory ⋮ Monotonicity properties for solutions of renewal equations ⋮ Monotonicity and aging properties of random sums ⋮ On the integrated tail of the deficit in the renewal risk model ⋮ Some aging properties involved with compound geometric distributions ⋮ A note on convolutions of compound geometric distributions

Cites Work

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• Risk theory for the compound Poisson process that is perturbed by diffusion
• Error bounds for exponential approximations of geometric convolutions
• Aspects of risk theory
• Compound geometric residual lifetime distributions and the deficit at ruin.
• Bounds on the tails of convolutions of compound distributions
• On higher-order properties of compound geometric distributions
• Approximation of the queue-length distribution of an M/GI/s queue by the basic equations
• Generalizations of the Pollaczek-Khinchin integral equation in the theory of queues
• Preservation of certain classes of life distributions under Poisson shock models
• NWU property of a class of random sums
• Foundations of queueing theory

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