Estimating Parameters Of Lognormal Distribution Using The Method Of L-Moments
Abstract
Commonly used statistical procedure to describe the observed statistical sets is to use their conventional moments or cumulants. An alternative approach is based on the use of other characteristics, which we call L-moments. L-moments are analogous to conventional moments, but they are based on linear combinations of order statistics, i.e., L-statistics. Using L-moments is theoretically preferable to the conventional moments and consists in the fact that L-moments characterize a wider range of distribution. When estimating from sample L-moments, L-moments are more robust to the presence of outliers in the data. Experience also shows that, compared to conventional moments, L-moments are less prone to bias of estimation. Parameter estimates obtained using L-moments are mainly in the case of small samples often even more accurate than estimates of parameters made by maximum likelihood method. This paper deals with the use of L-moments in the case of large data sets of income distribution (individual data) and wage distribution (data are ordered to the form of interval frequency distribution of extreme open intervals). The data for this research concern the Czech Republic and has been obtained from the Czech Statistical Office. Three-parametric lognormal curves were used as the model in all cases.
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