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Computation of optimal plotting points based on Pitman closeness with an application to goodness-of-fit for location-scale families


  • Balakrishnan, N.
  • Davies, K.F.
  • Keating, J.P.
  • Mason, R.L.


Plotting points of order statistics are often used in the determination of goodness-of-fit of observed data to theoretical percentiles. Plotting points are usually determined by using nonparametric methods which produce, for example, the mean- and median-ranks. Here, we use a distribution-based approach which selects plotting points (quantiles) based on the simultaneous-closeness of order statistics to population quantiles. We show that the plotting points so determined are robust over a multitude of symmetric distributions and then demonstrate their usefulness by examining the power properties of a correlation goodness-of-fit test for normality.

Suggested Citation

  • 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.
  • Handle: RePEc:eee:csdana:v:56:y:2012:i:9:p:2637-2649
    DOI: 10.1016/j.csda.2012.02.021

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    References listed on IDEAS

    1. 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.
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