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Independent poisson processes generated by record values and inter-record times

Author

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  • Stam, A. J.

Abstract

The mth-order upper record values of a sequence of independent random variables with common continuous distribution function, that are kth but not (k-1)th-order record values and that precede inter-record times of length j, form a Poisson process, the processes for different (k,j) being independent, k = 1,..., m, j = 1,2,... The records with record epochs after r\2>m, have a similar property if we condition with respect to the mth decreasing order statistic of the sample for times 1,..., r. These results extend theorems by Ignatov.

Suggested Citation

  • Stam, A. J., 1985. "Independent poisson processes generated by record values and inter-record times," Stochastic Processes and their Applications, Elsevier, vol. 19(2), pages 315-325, April.
    • Handle: RePEc:eee:spapps:v:19:y:1985:i:2:p:315-325
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    Cited by:

    1. Raqab, Mohammad Z., 1997. "Bounds based on greatest convex minorants for moments of record values," Statistics & Probability Letters, Elsevier, vol. 36(1), pages 35-41, November.

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