LQ-moments: Analogs of L-moments

The L-moments, certain linear functions of the expectations of order statistics, were introduced by and comprehensively reviewed by . L-moments have found wide applications in such fields of applied research as civil engineering, meteorology, and hydrology. We present a class of their analogs, labeled LQ-moments, obtained by replacing the expectations by functionals inducing quick estimators such as the median, Gastwirth estimator and the trimean. The LQ-moments always exist and are simpler to evaluate and estimate. The measures of skewness and kurtosis based on the LQ-moments can be used as more convenient and effective alternatives to the traditional beta coefficients. Simple explicit schemes for their estimation using readily obtainable sample quantiles are presented. The simplicity of their analyses is demonstrated in terms of the asymptotic distributions of the estimators of the LQ-moments, LQ-skewness and LQ-kurtosis. An application to the extreme value problem in flood data analysis in hydrology is discussed, and several potential applications are outlined.