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Further Results on Order Statistics Generated by Two Simulation Methods |
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| Authors: | W. Volterman E. Cramer K. F. Davies N. Balakrishnan |
| Affiliation: | 1. Department of Mathematics &2. Statistics, McMaster University, Hamilton, ON, Canadavolterwd@math.mcmaster.ca;4. Institute of Statistics, RWTH Aachen University, Aachen, Germany;5. Department of Statistics, University of Manitoba, Winnipeg, Manitoba, Canada;6. Statistics, McMaster University, Hamilton, ON, Canada;7. Department of Statistics, King Abdulaziz University, Jeddah, Saudi Arabia |
| 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. |