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Randomly Stopped \({\varvec{k}}\)th Order Statistics

  • Sandra MendonçaEmail author
  • Dinis Pestana
  • M. Ivette Gomes
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 136)

Abstract

Randomly stopped order statistics when the stopping rule is generated by a basic count distribution are investigated. Unified expressions in terms of the subordinator are presented, extending results from geometrically thinned sequences. Using the results on limit stable distributions for max-geometric laws, and Smirnov’s techniques to deal with limit laws of extreme order statistics, some results on stability of Panjer subordinated randomly stopped order statistics are discussed.

Keywords

Randomly stopped order statistics Panjer family Basic count distributions Order statistics Geometric thinning 

Notes

Acknowledgments

The authors are grateful to the referees for many valuable suggestions that have been used to improve the presentation of the paper. Professor Sneh Gulati’s very thorough proofreading of the text is gratefully acknowledged.

This research has been supported by National Funds through FCT – Fundação para a Ciência e a Tecnologia, projects PEst-OE/MAT/UI0006/2011, PEst-OE/MAT/UI0006/2014, and EXTREMA, PTDC /MAT /101736/2008.

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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Sandra Mendonça
    • 1
    • 2
    Email author
  • Dinis Pestana
    • 3
    • 4
  • M. Ivette Gomes
    • 3
    • 4
  1. 1.CCEEUniversidade da MadeiraFunchalPortugal
  2. 2.CEAULUniversidade de LisboaLisbonPortugal
  3. 3.CEAUL and DEIO–FCULUniversidade de LisboaLisbonPortugal
  4. 4.Instituto de Investigação Científica Bento da Rocha CabralLisbonPortugal

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