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Inverse renewal thinning of Cox and renewal processes

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  • Teke, S.P.
  • Deshmukh, S.R.

Abstract

A key result giving inter-connection amongst Bernstein function, completely monotone function and Stieltjes transform is established and used to derive sufficient conditions for the closure of the class of renewal processes under inverse renewal thinning. It is further proved that the class of Cox and renewal processes is closed under inverse renewal thinning for Bernoulli thinning, truncated negative binomial and truncated Poisson thinning.

Suggested Citation

  • Teke, S.P. & Deshmukh, S.R., 2008. "Inverse renewal thinning of Cox and renewal processes," Statistics & Probability Letters, Elsevier, vol. 78(16), pages 2705-2708, November.
    • Handle: RePEc:eee:stapro:v:78:y:2008:i:16:p:2705-2708
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    References listed on IDEAS

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    1. Yannaros, Nikos, 1989. "On Cox and renewal processes," Statistics & Probability Letters, Elsevier, vol. 7(5), pages 431-433, April.
    2. Nikos Yannaros, 1994. "Weibull renewal processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 46(4), pages 641-648, December.
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