Bias, Precision, and Accuracy of Skewness and Kurtosis Estimators for Frequently Used Continuous Distributions.

Abstract

Several measures of skewness and kurtosis were proposed by Hogg (1974) in order to reduce the bias of conventional estimators when the distribution is non-normal. Here we conducted a Monte Carlo simulation study to compare the performance of conventional and Hogg’s estimators, considering the most frequent continuous distributions used in health, education, and social sciences (gamma, lognormal and exponential distributions). In order to determine the bias, precision and accuracy of the skewness and kurtosis estimators for each distribution we calculated the relative bias, the coe cient of variation, and the scaled root mean square error. The e ect of sample size on the estimators is also analyzed. In addition, a SAS program for calculating both conventional and Hogg’s estimators is presented. The results indicated that for the non-normal distributions investigated, the estimators of skewness and kurtosis which best reflect the shape of the distribution are Hogg’s estimators. It should also be noted that Hogg’s estimators are not as a ected by sample size as are conventional estimators.