TL-Moments and LQ-Moments of the Exponentiated Pareto Distribution

The main concern of this paper is to derive the TL-moments (Trimmed Linear moments) of the exponentiated Pareto distribution (EPD) and use the TL-moments to estimate the unknown parameters of the EPD. Many special cases may be obtained such as L-moments (Linear moments), LH-moments (Linear Higher moments) and LL-moments (Linear Lower moments). Also, the LQ-moments (Linear Quantile moments) with the three cases (trimean, median and Gastwirth) will be obtained and used to estimate the unknown parameters of the EPD. The estimation of the EPD parameters is studied in numerical simulations where the method for obtaining TL-moment estimators is compared with other estimation methods (L-moment estimators, LQ-moment [trimean, median and Gastwirth] estimators, maximum likelihood estimators and the method of moment estimators). According to these comparisons, it is suggested that the method of L-moments is preferable for small sample size.