SAMPLE SIZES FOR APPROXIMATE INDEPENDENCE BETWEEN SAMPLE MEDIAN AND LARGEST (OR SMALLEST) ORDER STATISTIC.
Abstract
Let X sub 1 = or <...= or < X sub (2n + 1) be the order statistics for a random sample of size 2n + 1. Asymptotically, X sub(n + 1) and X sub(2n + 1) are independent. That is, the maximum of the differences between P(X sub(n + 1) = or < sub(n +1), X sub(2n + 1) = or < X sub(2n +1)) and the corresponding values assuming independence tends to zero as n approaches infinity. A minimum sample size is (approximately) determined which assures that the maximum difference is at most a stated amount. This minimum sample size is the smallest allowable for continuous populations but smaller sample sizes could possibly be usable for discontinuous cases. Likewise, X sub 1 is asymptotically independent of X sub(n + 1) and this same minimum sample size is applicable for the stated maximum difference. The minimum sample size is finite for all nonzero maximum differences but is very large if the maximum difference is much smaller than .005. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 11, 1968
- Accession Number
- AD0678787
Entities
People
- John E. Walsh
Organizations
- Southern Methodist University