Further Results on Order Statistics Generated by Two Simulation Methods

Abstract

Uniform order statistics generated by two simulation methods are compared by means of Pitman’s measure of closeness. This measure, as a probability, is shown to be asymptotically 1/2. Some results are also established for fixed points of the cumulative distribution function (CDF) for a uniform order statistic. These fixed points are important for calculations involving the joint distribution of these order statistics.

Keywords:

• Fixed points
• Limiting distribution
• Order statistics
• Pitman’s measure of closeness
• Simulation methods.

Mathematics Subject Classification:

• 62G30
• 65C10.