On some expressions for variance, covariance, skewness and L-moments (Q1888854)

The present paper provides a number of miscellaneous novel results concerning expressions of sample quantities and/or their population counterparts of continuous distributions. Section 2 gives interesting decomposition formulae of both sample and population variance, based on recent results of \textit{Y. G. Yatracos} [Proc. Am. Math. Soc. 126, No. 4, 1177--1179 (1998; Zbl 0896.62062); Sankhya, Ser. A 60, No. 1, 90--101 (1998; Zbl 0976.62007)]. Section 3 obtains similar decomposition expressions for the sample covariance and its population counterpart. Section 4 examines the single decomposition of population third central moments (as a skewness measure), in the same way to the population variance decomposition and based on a formula developed by \textit{M. C. Jones} and \textit{N. Balakrishnan} [J. Stat. Plann. Inference 103, No. 1--2, 377--390 (2002; Zbl 0988.62006)]. Section 5 displays an alternative proof for the general expression of L-moments [\textit{J. R. M. Hosking}, J. Econom. 73, No. 1, 261--284 (1996; Zbl 0854.62084)], followed in Section 6 by several basic inequalities concerning L-moments.