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Waiting times of exceedances in random threshold models

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  • Bairamov, Ismihan
  • EryIlmaz, Serkan

Abstract

Waiting time distributions associated with a sequence of binary trials have been widely studied and applied in various areas of probability and statistics. In this paper we study simple and compound waiting time random variables associated with random threshold models which make the elements of sequence dependent. The exact distributions are derived and the results are illustrated for random thresholds based on order statistics.

Suggested Citation

  • Bairamov, Ismihan & EryIlmaz, Serkan, 2009. "Waiting times of exceedances in random threshold models," Statistics & Probability Letters, Elsevier, vol. 79(5), pages 676-683, March.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:5:p:676-683
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    References listed on IDEAS

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    1. Jacek Wesołowski & Mohammad Ahsanullah, 1998. "Distributional Properties of Exceedance Statistics," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(3), pages 543-565, September.
    2. Ismihan Bairamov & Samuel Kotz, 2001. "On distributions of exceedances associated with order statistics and record values for arbitrary distributions," Statistical Papers, Springer, vol. 42(2), pages 171-185, April.
    3. S. Chakraborti & P. van der Laan & M. A. van de Wiel, 2004. "A class of distribution‐free control charts," Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 53(3), pages 443-462, August.
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    Cited by:

    1. Eryilmaz, Serkan & Gebizlioglu, Omer L. & Tank, Fatih, 2011. "Modeling of claim exceedances over random thresholds for related insurance portfolios," Insurance: Mathematics and Economics, Elsevier, vol. 49(3), pages 496-500.

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