Time spent below a random threshold by a Poisson driven sequence of observations

DOI10.1239/JAP/1059060907zbMath1049.60044OpenAlexW2082954176MaRDI QIDQ4462708

Jacek Wesołowski, Syed N. U. A. Kirmani

Publication date: 18 May 2004

Published in: Journal of Applied Probability (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1239/jap/1059060907

zbMATH Keywords

order statisticslimit theoremsnonhomogeneous Poisson processobservationsexceedance statisticsrandom threshold

Mathematics Subject Classification ID

Asymptotic distribution theory in statistics (62E20) Exact distribution theory in statistics (62E15) Extreme value theory; extremal stochastic processes (60G70) Processes in random environments (60K37) Applications of renewal theory (reliability, demand theory, etc.) (60K10) Point processes (e.g., Poisson, Cox, Hawkes processes) (60G55)

Related Items (2)

On the time spent below a random threshold by a system driven by a general counting process ⋮ Regressions for sums of squares of spacings

Cites Work

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• Distributional properties of exceedance statistics
• Distributional properties of statistics based on minimal spacing and record exceedance statistics
• Random threshold models based on multivariate observations.
• Shock models and wear processes
• On Repair Age Residual Repair Life in the Minimal Repair Process
• On distributions of exceedances associated with order statistics and record values for arbitrary distributions

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