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Extremes of random variables observed in renewal times

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  • Basrak, Bojan
  • Špoljarić, Drago

Abstract

We use point processes theory to describe the asymptotic distribution of all upper order statistics for observations collected at renewal times. As a corollary, we obtain limiting theorems for corresponding extremal processes.

Suggested Citation

  • Basrak, Bojan & Špoljarić, Drago, 2015. "Extremes of random variables observed in renewal times," Statistics & Probability Letters, Elsevier, vol. 97(C), pages 216-221.
    • Handle: RePEc:eee:stapro:v:97:y:2015:i:c:p:216-221
    DOI: 10.1016/j.spl.2014.11.025
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    References listed on IDEAS

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    1. Ward Whitt, 1980. "Some Useful Functions for Functional Limit Theorems," Mathematics of Operations Research, INFORMS, vol. 5(1), pages 67-85, February.
    2. Pancheva, Elisaveta & Mitov, Ivan K. & Mitov, Kosto V., 2009. "Limit theorems for extremal processes generated by a point process with correlated time and space components," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 390-395, February.
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    Cited by:

    1. Hees, Katharina & Nayak, Smarak & Straka, Peter, 2021. "Statistical inference for inter-arrival times of extreme events in bursty time series," Computational Statistics & Data Analysis, Elsevier, vol. 155(C).

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