LQ-Moments: Application to the Log-Normal distribution

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