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Exact distribution and Fisher information of weak record values

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  • Stepanov, A. V.
  • Balakrishnan, N.
  • Hofmann, Glenn

Abstract

We derive exact distributions of weak record values in lattice as well as non-lattice cases. We obtain the Fisher information contained in the first m weak records and the first m (strong) records from a discrete distribution. We give geometric and Poisson examples.

Suggested Citation

  • Stepanov, A. V. & Balakrishnan, N. & Hofmann, Glenn, 2003. "Exact distribution and Fisher information of weak record values," Statistics & Probability Letters, Elsevier, vol. 64(1), pages 69-81, August.
    • Handle: RePEc:eee:stapro:v:64:y:2003:i:1:p:69-81
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    References listed on IDEAS

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    1. Sen, Ananda & Balakrishnan, N., 1999. "Convolution of geometrics and a reliability problem," Statistics & Probability Letters, Elsevier, vol. 43(4), pages 421-426, July.
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    Cited by:

    1. Hofmann, Glenn & Balakrishnan, N. & Ahmadi, Jafar, 2005. "Characterization of hazard function factorization by Fisher information in minima and upper record values," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 51-57, April.
    2. Dembinska, A. & Stepanov, A., 2006. "Limit theorems for the ratio of weak records," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1454-1464, August.
    3. Krzysztof Jasiński, 2018. "Relations for product moments and covariances of kth records from discrete distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 125-141, February.
    4. S. Baratpour & J. Ahmadi & N. Arghami, 2007. "Entropy properties of record statistics," Statistical Papers, Springer, vol. 48(2), pages 197-213, April.
    5. Gouet, Raúl & Javier López, F. & Sanz, Gerardo, 2008. "Laws of large numbers for the number of weak records," Statistics & Probability Letters, Elsevier, vol. 78(14), pages 2010-2017, October.
    6. Gouet, Raúl & López, F. Javier & Maldonado, Lina P. & Sanz, Gerardo, 2014. "Statistical inference for the geometric distribution based on δ-records," Computational Statistics & Data Analysis, Elsevier, vol. 78(C), pages 21-32.
    7. Balakrishnan, N. & Stepanov, A., 2006. "On the Fisher information in record data," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 537-545, March.
    8. Enkelejd Hashorva & Alexei Stepanov, 2012. "Limit theorems for the spacings of weak records," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(2), pages 163-180, February.
    9. Amini, Morteza & Ahmadi, J., 2007. "Fisher information in record values and their concomitants about dependence and correlation parameters," Statistics & Probability Letters, Elsevier, vol. 77(10), pages 964-972, June.
    10. Bairamov, Ismihan & Stepanov, Alexei, 2006. "A note on large deviations for weak records," Statistics & Probability Letters, Elsevier, vol. 76(14), pages 1449-1453, August.

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