On Uncorrelated Linear Functions of Order Statistics

On Uncorrelated Linear Functions of Order Statistics of Independent But not Identically Distributed Random Variables

“…Further, it is pointed out in the above paper by means of an example that symmetry in the distribution is not necessary for zero correlation between the mean and the range of the sample. Aiyar(1963) examine the correlation between the mean and certain linear functions of ordered sample values for any population and derive the results for the symmetrical population as special case. In this paper the correlation between the pooled sample mean and certain linear functions of order statistics of inid random variables are obtained for pooled sample from populations with common location parameter µ and common scale parameter σ and the results if the parent distributions are symmetric about the common location parameter µ are derived therefrom.…”