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Pitman closeness of sample median to population median

Author

Listed:
  • Balakrishnan, N.
  • Iliopoulos, G.
  • Keating, J.P.
  • Mason, R.L.

Abstract

In this paper, Pitman closeness of order statistics to the median of a distribution is discussed. In particular, it is shown that the sample median is the Pitman-closest order statistic to the population median in some general situations, and expressions for probabilities of closeness are also derived.

Suggested Citation

  • Balakrishnan, N. & Iliopoulos, G. & Keating, J.P. & Mason, R.L., 2009. "Pitman closeness of sample median to population median," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1759-1766, August.
    • Handle: RePEc:eee:stapro:v:79:y:2009:i:16:p:1759-1766
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    Citations

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    Cited by:

    1. Balakrishnan, N. & Davies, K.F. & Keating, J.P. & Mason, R.L., 2012. "Computation of optimal plotting points based on Pitman closeness with an application to goodness-of-fit for location-scale families," Computational Statistics & Data Analysis, Elsevier, vol. 56(9), pages 2637-2649.
    2. Behboodian, J. & Bansal, Naveen & Hamedani, G.G. & Volkmer, Hans, 2013. "The Pitman inequality for exchangeable random vectors," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1825-1829.
    3. Ahmadi, Jafar & Balakrishnan, N., 2010. "Pitman closeness of current records for location-scale families," Statistics & Probability Letters, Elsevier, vol. 80(21-22), pages 1577-1583, November.
    4. Razmkhah, M. & Ahmadi, Jafar, 2013. "Pitman closeness of current k-records to population quantiles," Statistics & Probability Letters, Elsevier, vol. 83(1), pages 148-156.
    5. Balakrishnan, N. & Davies, Katherine F., 2013. "Pitman closeness results for Type-I censored data from exponential distribution," Statistics & Probability Letters, Elsevier, vol. 83(12), pages 2693-2698.

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