LQ-Moments: Application to the Log-Normal distribution

Abstract

Mudolkar and Hutson (1998) extended L-moments to new moment like entitles called LQmoments&#13; (LQMOM). The LQMOM are constructed by using functional defining the quick estimators,&#13; where the parameters of quick estimator take the values <i>p</i> = 0, &#945; = 1 for the median,&#13; p = 1/4, &#945; = 1/4 for the trimean and p = 0.3, &#945; = 1/3 for the Gastwirth, in places of&#13; expectations in L-moments (LMOM). The objective of this paper is to develop improved LQMOM&#13; that do not impose restrictions on the value of <i>p</i> and &#945; such as the median, trimean or the Gastwirth&#13; but we explore an extended class of LQMOM with consideration combinations of <i>p</i> and &#945; values in&#13; the range 0 and 0.5. The popular quantile estimator namely the weighted kernel quantile (WKQ)&#13; estimator will be proposed to estimate the quantile function. Monte Carlo simulations are conducted to&#13; illustrate the performance of the proposed estimators of the log-normal 3 (LN3) distribution were&#13; compared with the estimators based on conventional LMOM and MOM (method of moments) for&#13; various sample sizes and return periods