A comparative analysis of L-moments, maximum likelihood, and maximum product of spacing methods for the four-parameter kappa distribution in extreme value analysis.

The study has investigated the implications of three estimation methods, namely L-moments, Maximum Likelihood, and Maximum Product of Spacing (MPS), for fitting the four-parameter Kappa Distribution (KAPD) in extreme value analysis using Monte Carlo simulations. The accuracy of the estimates has been evaluated using root mean square error (RMSE) and bias. The paper also includes an analysis of the effect of the estimation method on the estimated quantiles considering a real-life example of annual maximum peak flows and the Generalized Normal Distribution as the error distribution. Assessment metrics of the empirical analysis include standard error, L-scale, and 90% confidence limits of the estimated quantiles. The results reveal that MPS is a preferred method of estimation of parameters for KAPD, i.e. having the lowest RMSE values, especially in the presence of heavier tail and significant positive skewness for small to very large sample sizes. Secondly, the method of L-moments is recommended due to its low bias while analyzing the distribution of shape parameters having a slightly heavier tail, and slight or moderate positive skewness. The results associated with the quality of estimated quantiles using real-life data are consistent with the findings of simulation outcomes.