On some expressions for variance, covariance, skewness and L-moments
type: Item
instance of: scholarly article
title: On some expressions for variance, covariance, skewness and L-moments
zbMATH Open document ID: 1057.62012
author: M. C. Jones
published in: Journal of Statistical Planning and Inference
publication date: 2004-11-29T00:00:00Z
review text: 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.
reviewed by: Neculai Curteanu
Mathematics Subject Classification ID: 62E15
Mathematics Subject Classification ID: 60E05
Mathematics Subject Classification ID: 60E15
zbMATH DE Number: 2119601
zbMATH Keywords: mean residual life
zbMATH Keywords: moments
zbMATH Keywords: sample and population variance formulas
zbMATH Keywords: sample and population coveriance formulas
zbMATH Keywords: population third central moment
zbMATH Keywords: L-moment inequalities
describes a project that uses: LMOMENTS
MaRDI profile type: Publication
full work available at URL: j.jspi.2003.09.001
OpenAlex ID: W2030797447
cites work: Q5342246
cites work: Variability orders and mean differences
cites work: Q5629053
cites work: Q3482696
cites work: How are moments and moments of spacings related to distribution functions?
cites work: Derivation of approximants to the inverse distribution function of a continuous univariate population from the order statistics of a sample
cites work: Variance and clustering
DOI: 10.1016/J.JSPI.2003.09.001
description: scientific article; zbMATH DE number 2119601