EXACT EXISTENCE OF EVERY POSSIBLE DISTRIBUTION FOR ANY SAMPLE ORDER STATISTIC.
Themis Signal Analysis Statistics Research Program,
SOUTHERN METHODIST UNIV DALLAS TEX DEPT OF STATISTICS
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Given are any stated value for sample size and an arbitrary but specified univariate distribution. Let an arbitrary but specified order statistic for a univariate random sample of this size be considered. It is shown that a statistical population always exists, for yielding the sample, such that the distribution of the order statistic is exactly the specified distribution. Some asymptotic implications of these results are outlined. Author
- Statistics and Probability