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Random and Poisson paced record models in the Fα setup

Part of: Distribution theory Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Glenn Hofmann  and
H. N. Nagaraja
Glenn Hofmann*
Affiliation:
Universidad de Concepción
H. N. Nagaraja*
Affiliation:
Ohio State University
*
∗Postal address: Departamento de Estadistica, Facultad de Ciencias Fisicas y Matematicas, Casilla 4009, Barrio Universitario, Concepción, Chile. Email address: glenn@gauss.cfm.udec.cl.
∗∗Postal address: Department of Statistics, Ohio State University, Columbus, OH 43210-1247, USA. Email address: hnn@stat.ohio-state.edu.
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Abstract

We study a random record model where the observation Xi has continuous distribution function Fαi (αi > 0) and the number of available observations is random and independent of the observations. We obtain the joint distribution of the record values and inter-record times for our model. We investigate the distribution of the number of records when the number of observations has one of the common distributions and the α's increase geometrically or linearly. A particularly interesting case arises when the observations arrive at time points paced by a Poisson point process. For this model we obtain distributional results for the inter-arrival times of records for a large class of combinations of α structures and intensity functions.

Keywords

Record timesrecord countsrecord valuesinter-record timesPoisson processrandom record modelstochastic convergence

MSC classification

Primary: 60G70: Extreme value theory; extremal processes 60G55: Point processes
Secondary: 62E15: Exact distribution theory 62E20: Asymptotic distribution theory
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 2 , June 2000 , pp. 374 - 388
Copyright
Copyright © by the Applied Probability Trust 2000 

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Footnotes

Supported in part by FONDECYT grant Number 1990343 of Chile.

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