A simulation study of some sample measures of skewness

Holgersson (2010) has proposed a modified skewness measure “θ”that is based on the pearson measure and the classical measure. he has claimed that the modified skewness measure uniquely determines the symmetry of variable for a wide range of distributions. however,he ignored in his study,the recently introduced measures. it is well known that the classical measure of skewness,=μ3/σ3 measured by the standardized third moment is criticized in the literature. it is established that the pearson measure does not portray skewness correctly in some situations and it does not preserve the ordering of skewness. the measure introduced by holgersson (2010) inherits the drawbacks of both the classical and the pearson measures of skewness. doane and seward (2011) have advocated the use of pearson measure of skewness because it is simple to compute and interpret. in the last two decades,a number of new measures of skewness have been introduced for a population data. however,sample versions of some measures of skewness are not discussed as their sampling distributions are not easy to obtain. recently,habib (2011) has obtained the sampling distribution of the sample version of the modified skewness measure “γt” introduced by tajuddin (1999). in this paper,we examine the performance of different measures of sample skewness by means of a simulation study and their applications on some real life data. we find that the sample version of the modified skewness measure “γt ” introduced by tajuddin (1999) performs at least better than the pearson measure and it is simpler in computation and easier in interpretation than the pearson measure of skewness. this measure performs better than classical measure and its modification given by holgersson (2010),in the presence of outliers. © 2016 pakistan journal of statistics