A Note on the Comparison between Simple Mean and Mean Based on Distinct Units in Sampling with Replacement

Authors
Asok, C.
Citation
C. Asok,, A Note on the Comparison between Simple Mean and Mean Based on Distinct Units in Sampling with Replacement, American statistician , 34(3), 1980, pp. 158-158
Journal title
American statistician → ACNP
ISSN journal
00031305
Volume
34
Issue
3
Year of publication
1980
Pages
158 - 158
Database
ACNP
SICI code
Abstract
Basu (1958) and Raj and Khamis (1958) have shown that in sampling with replacement the average over distinct units possesses lower variance than the average over the entire sample, including repetitions.While Basu proves the result by the use of the Rao-Blackwell theorem, Raj and Khamis prove it by making use of the distribution of the number of distinct units u in the sample, and the proof is quite involved.Here, an elementary algebraic proof is given.