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doi:10.1016/0167-7152(82)90018-9 
Copyright © 1982 Published by Elsevier Science B.V.
A quantile domain perspective on the relationships between optimal grouping, spacing and stratification problems
Available online 17 April 2003.
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Abstract
The relationships between two distributions having the same solutions for problems of optimal spacing selection for the asymptotically best linear unbiased estimator of a location or scale parameter or for problems of optimal stratification for estimation of a population mean are investigated. Easily checked necessary and sufficient conditions under which two distributions have identical solutions to these problems are given in terms of their quantile and density-quantile functions. As an application of these results a quantile domain analoque of a theorem due to Adatia and Chan (1981) on the equivalence of optimal grouping, spacing and stratification problems is obtained.
Author Keywords: Approximation; density-quantile function; quantile function; optimal grouping; optimal spacing; optimal stratification
