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Asymptotic results for linear combinations of spacings generated by i.i.d. exponential random variables

Author

Listed:
  • Camilla Calì

    (Università di Napoli Federico II, Via Cintia)

  • Maria Longobardi

    (Università di Napoli Federico II, Via Cintia)

  • Claudio Macci

    (Università di Roma Tor Vergata, Via della Ricerca Scientifica)

  • Barbara Pacchiarotti

    (Università di Roma Tor Vergata, Via della Ricerca Scientifica)

Abstract

We prove large (and moderate) deviations for a class of linear combinations of spacings generated by i.i.d. exponentially distributed random variables. We allow a wide class of coefficients which can be expressed in terms of continuous functions defined on [0, 1] which satisfy some suitable conditions. In this way we generalize some recent results by Giuliano et al. (J Statist Plann Inference 157–158:77–89, 2015) which concern the empirical cumulative entropies defined in Di Crescenzo et al. (J Statist Plann Inference 139:4072–4087, 2009a).

Suggested Citation

  • Camilla Calì & Maria Longobardi & Claudio Macci & Barbara Pacchiarotti, 2022. "Asymptotic results for linear combinations of spacings generated by i.i.d. exponential random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(6), pages 733-752, August.
    • Handle: RePEc:spr:metrik:v:85:y:2022:i:6:d:10.1007_s00184-021-00849-8
    DOI: 10.1007/s00184-021-00849-8
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    References listed on IDEAS

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    1. Bruce Jones & Ričardas Zitikis, 2003. "Empirical Estimation of Risk Measures and Related Quantities," North American Actuarial Journal, Taylor & Francis Journals, vol. 7(4), pages 44-54.
    2. Bryc, Wlodzimierz, 1993. "A remark on the connection between the large deviation principle and the central limit theorem," Statistics & Probability Letters, Elsevier, vol. 18(4), pages 253-256, November.
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