Summary
We consider a general definition of record-like observations and present a methodology based on martingales to describe the asymptotic behavior of the corresponding counting process. Our definition includes not only the well-known records and near-records, from continuous or discrete distributions. It also contains, as particular cases of interest, weak records and geometric records. We provide concrete examples and discuss possible extensions and alternative approaches. We also propose some problems for future work.
To Marisa. We thank the editors for giving us the opportunity to participate in this tribute to Marisa Manéndez.
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Gouet, R., López, F.J., Sanz, G. (2011). On Record-Like Observations: Asymptotic Analysis Using Martingale Tools. In: Pardo, L., Balakrishnan, N., Gil, M.Á. (eds) Modern Mathematical Tools and Techniques in Capturing Complexity. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-20853-9_27
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DOI: https://doi.org/10.1007/978-3-642-20853-9_27
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