Investigation and comparison of sampling properties of L-moments and conventional moments

The first part of this article deals with fitting of regression equations for the sampling properties, variance of L-standard deviation (l2), and bias and variance of L-skewness (t3), based on Monte-Carlo simulation results, for generalised Normal (Lognormal-3) and Pearson-3 distributions. These fitted equations will be useful in formulating goodness-of-fit test statistics in regional frequency analysis. The second part presents a comparison of the sampling properties between L-moments and conventional product moments for generalised Normal, generalised Extreme Value, generalised Pareto and Pearson-3 distributions, in a relative form. The comparison reveals that the bias in L-skewness is found to be insignificant up to a skewness of about 1.0, even for small samples. In case of higher skewness, for a reasonable sample size of 30, L-skewness is found to be nearly unbiased. However, the conventional skewness is found to be significantly biased, even for a low skewness of 0.5 and a reasonable sample size of 30. The overall performance evaluation in terms of 'Relative-RMSE in third moment ratio' reveals that conventional moments are preferable at lower skewness, particularly for smaller samples, while L-moments are preferable at higher skewness, for all sample sizes. This point is illustrated through an application that seeks to obtain an appropriate regional flood frequency distribution for the 98 catchment areas located in the central region of India, spread over six hydrometeorologic subzones.