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An Operator Property of the Distribution of a Nonhomogeneous Poisson Process with Applications

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  • Georgios Psarrakos

    (University of Piraeus)

Abstract

A class of integral operators is considered, and a semi-preserving property for the tail distribution of a nonhomogeneous Poisson process is obtained. This new result is applied to the equilibrium and length-biased tail distributions, and some characterization results are studied. Numerical examples are also given to evaluate our results.

Suggested Citation

  • Georgios Psarrakos, 2016. "An Operator Property of the Distribution of a Nonhomogeneous Poisson Process with Applications," Methodology and Computing in Applied Probability, Springer, vol. 18(4), pages 1197-1215, December.
    • Handle: RePEc:spr:metcap:v:18:y:2016:i:4:d:10.1007_s11009-015-9466-3
    DOI: 10.1007/s11009-015-9466-3
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    References listed on IDEAS

    as
    1. Georgios Psarrakos & Jorge Navarro, 2013. "Generalized cumulative residual entropy and record values," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(5), pages 623-640, July.
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    7. Landriault, David & Willmot, Gordon, 2008. "On the Gerber-Shiu discounted penalty function in the Sparre Andersen model with an arbitrary interclaim time distribution," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 600-608, April.
    8. Dickson, David C. M. & Hipp, Christian, 2001. "On the time to ruin for Erlang(2) risk processes," Insurance: Mathematics and Economics, Elsevier, vol. 29(3), pages 333-344, December.
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