An Evaluation of Two Model Specification Techniques for a Lognormal Distribution

Two frequently used statistical estimation techniques are applied to the lognormal distribution with unit shape-parameter. The first technique involves comparing sample estimates of skewness and kurtosis with their corresponding population values in order to determine the suitability of the distribution as a model for a set of empirical data. The sample skewness and kurtosis for samples of moderate size provide biased downward estimates of the population values. This bias can be considered if this technique is applied to a data set by using results presented in this paper. The second technique is probability plotting. The recommended plotting position is (i -0.5)/n. An evaluation of the graphical estimators shows that they are substantially inferior to the best linear unbiased estimators and Blom's estimators. The results are applied to a data set consisting of automotive emissions.