Pitman Closeness of Order Statistics to Population Quantiles

Abstract

In this article, Pitman closeness of sample order statistics to population quantiles of a location-scale family of distributions is discussed. Explicit expressions are derived for some specific families such as uniform, exponential, and power function. Numerical results are then presented for these families for sample sizes n = 10,15, and for the choices of p = 0.10, 0.25, 0.75, 0.90. The Pitman-closest order statistic is also determined in these cases and presented.

Keywords:

• Order statistics
• Pitman closeness
• Pitman-closest order statistic
• Probabilities of closeness
• Quantiles

Mathematics Subject Classification:

• 62F10
• 62G05
• 62G30

Acknowledgments

The authors express their sincere thanks to the referee for making some useful suggestions which led to an improvement in the presentation of this article. The first author acknowledges support from NSERC for funding this research, and the second author thanks the University of Manitoba.