Just a moment!

Abstract

The distribution functions for three statistics, the mean, standard deviation, and coefficient of skewness, for small samples from various distributions were obtained by Monte Carlo experiments. Sample sizes of 10 (10) 90 were considered, and the distributions used were the normal, Gumbel (extreme value type 1), log normal, Pearson type 3 (gamma), Weibull, and Pareto type 1 (Pearson type 4). Values of the coefficient of skewness used in generating the samples were in the range [0.0, 15.0]. Pronounced skews, biases, and constraints in the sampling properties of the statistics were observed. Examples of the available graphs of the distribution functions are presented.