Open Access
2024 Random permutations generated by delay models and estimation of delay distributions
Ludwig Baringhaus, Rudolf Grübel
Author Affiliations +
Electron. J. Statist. 18(1): 167-190 (2024). DOI: 10.1214/23-EJS2205


Objects arrive at a system at times U1,U2, and leave at times U1+X1,U2+X2,, where we assume that the arrivals are independent and uniformly distributed on the unit interval, that the delay times are independent with distribution function G, and that arrival and delay times are independent. Let Πn be the random permutation that connects the ranks of the first n arrivals and departures. We investigate the use of Πn for estimating G. We consider empirical copulas in the nonparametric and pattern frequencies in the parametric situation.


Constructive comments by an anonymous referee have led to a considerable improvement of the paper.


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Ludwig Baringhaus. Rudolf Grübel. "Random permutations generated by delay models and estimation of delay distributions." Electron. J. Statist. 18 (1) 167 - 190, 2024.


Received: 1 March 2023; Published: 2024
First available in Project Euclid: 30 January 2024

Digital Object Identifier: 10.1214/23-EJS2205

Primary: 62G20
Secondary: 05A05

Keywords: delay copula , monotone minorant estimator , nonparametric estimation , Parametric estimation , Pattern , random permutation , rank plot , Service time distribution

Vol.18 • No. 1 • 2024
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