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Limit theorems for runs based on 'small spacings'

Author

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  • Stepanov, A.

Abstract

A new concept of runs was proposed in the work of Eryilmaz and Stepanov (2008). A sequence of spacings forms a run if the lengths of these spacings do not exceed [epsilon]>0. In that paper, asymptotic properties of such spacings were investigated and statistical criteria proposed. In our present study, we maintain research on runs associated with these spacings. We derive limit theorems for the total number of runs, longest run and propose a statistical criterion.

Suggested Citation

  • Stepanov, A., 2011. "Limit theorems for runs based on 'small spacings'," Statistics & Probability Letters, Elsevier, vol. 81(1), pages 54-61, January.
    • Handle: RePEc:eee:stapro:v:81:y:2011:i:1:p:54-61
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    References listed on IDEAS

    as
    1. Serkan Eryılmaz & Alexei Stepanov, 2008. "Runs in an ordered sequence of random variables," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 67(3), pages 299-313, April.
    2. Balakrishnan, N. & Stepanov, A., 2004. "A note on the paper of Khmaladze et al," Statistics & Probability Letters, Elsevier, vol. 68(4), pages 415-419, July.
    3. Serkan Eryilmaz, 2005. "On the distribution and expectation of success runs in nonhomogeneous Markov dependent trials," Statistical Papers, Springer, vol. 46(1), pages 117-128, January.
    4. Li, Yun, 1999. "A note on the number of records near the maximum," Statistics & Probability Letters, Elsevier, vol. 43(2), pages 153-158, June.
    5. Etemadi, Nasrollah, 1983. "On the laws of large numbers for nonnegative random variables," Journal of Multivariate Analysis, Elsevier, vol. 13(1), pages 187-193, March.
    6. Ahmad, Ibrahim A. & Kochar, Subhash C., 1988. "Testing for dispersive ordering," Statistics & Probability Letters, Elsevier, vol. 7(3), pages 179-185, December.
    7. Eryilmaz, Serkan, 2007. "Extension of runs to the continuous-valued sequences," Statistics & Probability Letters, Elsevier, vol. 77(4), pages 383-388, February.
    Full references (including those not matched with items on IDEAS)

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