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Sharp Bounds for Exponential Approximations of NWUE Distributions

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  • Mark Brown

    (Columbia University)

  • Shuangning Li

    (Stanford University)

Abstract

Let F be an NWUE distribution with mean 1 and G be the stationary renewal distribution of F. We would expect G to converge in distribution to the unit exponential distribution as its mean goes to 1. In this paper, we derive sharp bounds for the Kolmogorov distance between G and the unit exponential distribution, as well as between G and an exponential distribution with the same mean as G. We apply the bounds to geometric convolutions and to first passage times.

Suggested Citation

  • Mark Brown & Shuangning Li, 2018. "Sharp Bounds for Exponential Approximations of NWUE Distributions," Methodology and Computing in Applied Probability, Springer, vol. 20(3), pages 875-896, September.
    • Handle: RePEc:spr:metcap:v:20:y:2018:i:3:d:10.1007_s11009-017-9596-x
    DOI: 10.1007/s11009-017-9596-x
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    References listed on IDEAS

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    1. Aldous, David J. & Brown, Mark, 1993. "Inequalities for rare events in time-reversible Markov chains II," Stochastic Processes and their Applications, Elsevier, vol. 44(1), pages 15-25, January.
    2. Dickson, D. C. M., 2001. "Lundberg Approximations for Compound Distributions with Insurance Applications. By G. E. Willmot and X. S. Lin. (Springer, 2000)," British Actuarial Journal, Cambridge University Press, vol. 7(4), pages 690-691, October.
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    Cited by:

    1. Lesław Gajek & Marcin Rudź, 2020. "Finite-horizon general insolvency risk measures in a regime-switching Sparre Andersen model," Methodology and Computing in Applied Probability, Springer, vol. 22(4), pages 1507-1528, December.

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