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On uppermost discrete spacing

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  • Nevzorov, Valery B.
  • Stepanov, Alexei

Abstract

In this work, we investigate the properties of the uppermost spacing obtained from order statistics in the discrete case. We first define this random variable, derive its distribution function, and then study its asymptotic behavior. Finally, we present some examples illustrating the obtained asymptotic results.

Suggested Citation

  • Nevzorov, Valery B. & Stepanov, Alexei, 2024. "On uppermost discrete spacing," Statistics & Probability Letters, Elsevier, vol. 208(C).
    • Handle: RePEc:eee:stapro:v:208:y:2024:i:c:s0167715224000300
    DOI: 10.1016/j.spl.2024.110061
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    References listed on IDEAS

    as
    1. Pakhteev, A. & Stepanov, A., 2019. "Discrete records: Limit theorems for their spacings and generation methods," Statistics & Probability Letters, Elsevier, vol. 148(C), pages 134-142.
    2. Brands, J. J. A. M. & Steutel, F. W. & Wilms, R. J. G., 1994. "On the number of maxima in a discrete sample," Statistics & Probability Letters, Elsevier, vol. 20(3), pages 209-217, June.
    3. Beirlant, Jan & van Zuijlen, M. C. A., 1985. "The empirical distribution function and strong laws for functions of order statistics of uniform spacings," Journal of Multivariate Analysis, Elsevier, vol. 16(3), pages 300-317, June.
    4. M. Ahsanullah, 1984. "A characterization of the exponential distribution by higher order gap," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 31(1), pages 323-326, December.
    5. Stepanov, Alexei & Dembińska, Anna, 2022. "Limit theorems for the uppermost mth spacing based on weak geometric records," Statistics & Probability Letters, Elsevier, vol. 183(C).
    Full references (including those not matched with items on IDEAS)

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