Trimmed Linear Moments Approach to Estimation of Type II Extreme Value Distribution

Source abstract

The Type II Extreme Value distribution is widely applied in modelling extreme events in engineering, hydrology, and environmental studies. Accurate parameter estimation of this distribution remains essential, particularly under conditions of skewed data and the presence of outliers. Traditional estimation techniques such as the Method of Moments, Maximum Likelihood Estimation, and L-moments have been extensively used; however, they often exhibit limitations in efficiency, robustness, or computational stability. To address these challenges, this study examined the performance of Trimmed Linear Moments (1,1) as an alternative to conventional Linear moments for estimating the scale (σ) and shape (α) parameters of the Type II Extreme Value distribution. Monte Carlo simulation experiments were conducted for sample sizes and , and for fixed shape parameter values α = 2, 3 and 4, with scale parameters ranging from 0.3 to 1.5. the simulation was replicated 1000 times, and estimator performance was evaluated using mean squared error (MSE). The results consistently showed that both LM and TLM (1,1) estimators improved in accuracy as sample size increased, indicating asymptotic consistency. However, the TLM (1,1) method consistently produced smaller mean squared error MSE values than the conventional L-moments across all parameter settings and sample sizes. The study therefore recommends TLM (1,1) as a preferred estimation approach for modelling extreme value data.