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Pitman closeness of predictors of future order statistics for two parameter exponential distribution

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  • S. MirMostafaee
  • Jafar Ahmadi
  • Narjes Sadeghian

Abstract

In this paper, the Pitman closeness of predictors for a future order statistic coming from a two parameter exponential distribution is discussed. The optimum equivariant predictor using the Pitman closeness criterion is derived and compared with the best invariant predictor and the best unbiased predictor. The predictors are obtained on the basis of observed record values. Exact expressions for the required Pitman closeness probabilities are derived when both parameters are considered to be unknown. Similar results are obtained for the predictors of the mean of a future sample from exponential distribution. Several tables which contain numerical computations, are provided in order to compare the predictors in the sense of Pitman’s measure of closeness. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • S. MirMostafaee & Jafar Ahmadi & Narjes Sadeghian, 2015. "Pitman closeness of predictors of future order statistics for two parameter exponential distribution," Computational Statistics, Springer, vol. 30(4), pages 1163-1183, December.
    • Handle: RePEc:spr:compst:v:30:y:2015:i:4:p:1163-1183
    DOI: 10.1007/s00180-015-0554-1
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    References listed on IDEAS

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    1. Razmkhah, M. & Ahmadi, Jafar, 2013. "Pitman closeness of current k-records to population quantiles," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 148-156.
    2. Takada, Y., 1991. "Median unbiasedness in an invariant prediction problem," Statistics & Probability Letters, Elsevier, vol. 12(4), pages 281-283, October.
    3. Ahmadi, J. & MirMostafaee, S.M.T.K., 2009. "Prediction intervals for future records and order statistics coming from two parameter exponential distribution," Statistics & Probability Letters, Elsevier, vol. 79(7), pages 977-983, April.
    4. MirMostafaee, S.M.T.K. & Ahmadi, Jafar, 2011. "Point prediction of future order statistics from an exponential distribution," Statistics & Probability Letters, Elsevier, vol. 81(3), pages 360-370, March.
    5. Raqab, Mohammad Z. & Balakrishnan, N., 2008. "Prediction intervals for future records," Statistics & Probability Letters, Elsevier, vol. 78(13), pages 1955-1963, September.
    6. Mohammad Raqab & Jafar Ahmadi & Byan Arabli, 2013. "Comparisons among some predictors of exponential distributions using Pitman closeness," Computational Statistics, Springer, vol. 28(5), pages 2349-2365, October.
    7. Ahmadi, Jafar & Balakrishnan, N., 2009. "Pitman closeness of record values to population quantiles," Statistics & Probability Letters, Elsevier, vol. 79(19), pages 2037-2044, October.
    8. 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.
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