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Statistical inference for the geometric distribution based on δ-records

Author

Listed:
  • Gouet, Raúl
  • López, F. Javier
  • Maldonado, Lina P.
  • Sanz, Gerardo

Abstract

New inferential procedures for the geometric distribution, based on δ-records, are developed. Maximum likelihood and Bayesian approaches for parameter estimation and prediction of future records are considered. The performance of the estimators is compared with those based solely on record-breaking data by means of Monte Carlo simulations, concluding that the use of δ-records is clearly advantageous. An example using real data is also discussed.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:78:y:2014:i:c:p:21-32
    DOI: 10.1016/j.csda.2014.04.002
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    References listed on IDEAS

    as
    1. 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.
    2. Sultan, K.S. & AL-Dayian, G.R. & Mohammad, H.H., 2008. "Estimation and prediction from gamma distribution based on record values," Computational Statistics & Data Analysis, Elsevier, vol. 52(3), pages 1430-1440, January.
    3. Soliman, Ahmed A. & Abd Ellah, A.H. & Sultan, K.S., 2006. "Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches," Computational Statistics & Data Analysis, Elsevier, vol. 51(3), pages 2065-2077, December.
    4. Raúl Gouet & F. López & Gerardo Sanz, 2012. "On δ-record observations: asymptotic rates for the counting process and elements of maximum likelihood estimation," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 188-214, March.
    5. 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.
    6. John F. Padgett & Doowan Lee & Nick Collier, 2003. "Economic production as chemistry," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 12(4), pages 843-877, August.
    7. 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.
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    Cited by:

    1. Fernando López-Blázquez & Begoña Salamanca-Miño, 2015. "Distribution theory of $$\delta $$ δ -record values: case $$\delta \ge 0$$ δ ≥ 0," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(3), pages 558-582, September.

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