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Improved estimators of the distribution function based on lower record values

Author

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  • R. Arabi Belaghi
  • M. Arashi
  • S. Tabatabaey

Abstract

In this paper, we define different types of estimators for the distribution function, namely preliminary test (PT), shrinkage PT (SPT), Stein type (S), and Thompson shrinkage (TS) estimators based on lower record observations and their inter record times. Their asymptotic distributional bias and mean square error are explicitly derived. The superiority conditions of the new proposed estimators over the existing estimator of distribution function are also obtained. It is shown that about the neighborhood of the null hypothesis $$F_0$$ F 0 , the PTE is superior to the SE in the sense of having higher asymptotic relative efficiency. Further for the reasonable values of $$\alpha $$ α the newly proposed SPT estimator uniformly dominates the non-parametric maximum like likelihood estimators in the literatures. A table is also given to be more specifics along the exhibited theoretical results for practical sake. Some graphical representations are given as proofs of our assertions. A simulation study is also carried out for some life time distribution, to examine the accuracy of the proposed estimators with a limited sample size. The results show that combination of the parametric and nonparametric estimators will give more efficient estimators. This study is finally concluded by applying the theoretic results to a real data set. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • R. Arabi Belaghi & M. Arashi & S. Tabatabaey, 2015. "Improved estimators of the distribution function based on lower record values," Statistical Papers, Springer, vol. 56(2), pages 453-477, May.
    • Handle: RePEc:spr:stpapr:v:56:y:2015:i:2:p:453-477
    DOI: 10.1007/s00362-014-0591-9
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    References listed on IDEAS

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    1. Balakrishnan, N. & Stepanov, A., 2006. "On the Fisher information in record data," Statistics & Probability Letters, Elsevier, vol. 76(5), pages 537-545, March.
    2. J. Ravichandran, 2012. "A review of preliminary test-based statistical methods for the benefit of Six Sigma quality practitioners," Statistical Papers, Springer, vol. 53(3), pages 531-547, August.
    3. Jafar Ahmadi & N. Balakrishnan, 2013. "On the nearness of record values to order statistics from Pitman’s measure of closeness," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 76(4), pages 521-541, May.
    4. B. Kibria & A. Saleh, 2010. "Preliminary test estimation of the parameters of exponential and Pareto distributions for censored samples," Statistical Papers, Springer, vol. 51(4), pages 757-773, December.
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    Cited by:

    1. A. Asgharzadeh & A. Fallah & M. Z. Raqab & R. Valiollahi, 2018. "Statistical inference based on Lindley record data," Statistical Papers, Springer, vol. 59(2), pages 759-779, June.
    2. A. Asgharzadeh & S. F. Bagheri & N. A. Ibrahim & M. R. Abubakar, 2020. "Optimal confidence regions for the two-parameter exponential distribution based on records," Computational Statistics, Springer, vol. 35(1), pages 309-326, March.

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