A very general measure of skewness based on the quantiles is introduced, which includes several well-known measures as special cases. Sample versions of our measure may be used as test statistics for testing the hypothesis of symmetry about an unknown value. We provide large sample theory for such a statistic and discuss the asymptotic relative efficiencies of this against some competing test statistics for symmetry. © 2012 Elsevier B.V..

A procedure, based on sample spacings, is proposed for testing whether a univariate distribution is symmetric about some unknown value. The proposed test is a modification of a sign test suggested by Antille and Kersting [1977. Tests for symmetry. Z. Wahrscheinlichkeitstheorie verw. Gebiete 39, 235-255], but unlike Antille and Kersting's test, our modified test is asymptotically distribution-free and is usable in practice. A simulation study indicates that the proposed test maintains the nominal level of significance, α fairly accurately even for samples of size as small as 20, and a comparison with the classical test based on sample coefficient of skewness, shows that our test has good power for detecting different asymmetric distributions. © 2006 Elsevier B.V. All rights reserved.

A two-term Edgeworth expansion for the standardized version of the sample total in a two-stage sampling design is derived. In particular, for the commonly used stratified and cluster sampling schemes, formal two-term asymptotic expansions are obtained for the Studentized versions of the sample total. These results are applied in conjunction with the bootstrap to construct more accurate confidence intervals for the unknown population total in such sampling schemes.