We studied the effects of sample size and distribution scale/shape for 3 types of skewness (g1, G1, and b1) and kurtosis (g2, G2, and b2) using 18 simulated probability distributions. In general, skewness and kurtosis always increased with increasing sample size. The order in the skewness coefficients over all distributions and parameters was typically b1, g1, G1. The same pattern was observed for kurtosis, for which order was b2, g2, G2. In terms of a change in sign, mean skewness values (g1, G1, b1) at low sample sizes were unreliable below n=50 for the Beta distribution and unreliable below n=100 for the Student's t and Laplace distributions. Mean kurtosis values for g2 and b2 but not G2 at the smallest samples size were unreliable for most distributions. In fact, b2 was less reliable than g2 for the Laplace, Erlang, exponential, power, and Weibull distributions. Skewness and kurtosis were also dependent on sample size. For skewness G1, the symmetric distributions (normal, Student's t, Laplace, and Logistic) had near-zero mean differences between samples size n=10 and n=100 for each of the scale/shape parameter values used. Whereas the stable, Pareto, and Weibull distributions had the greatest mean differences. Mean differences across sample size for kurtosis G2 within each scale/shape parameter were much greater, and this was also observed among symmetric distributions (Student's t, Laplace, Logistic). The greatest differences of kurtosis G2 across sample size were observed for the Student's t, stable, Pareto, and Weibull distributions. Regarding scale/shape, for skewness G1 the greatest variation was observed for the stable, Weibull, Pareto, and lognormal distributions. While for kurtosis G2, the greatest differences were observed for the Pareto, Weibull, Student's t, and lognormal distributions. The s.d. of skewness cluster analysis shows that the Weibull, and Student's t distributions were unlike any other distributions, since their s.d. decreased drastically with increasing parameter value. Lastly, the lognormal distribution was unlike any other distribution, since its s.d. of skewness greatly increased across increasing parameter values. Students and practitioners should be aware of the types of skewness and kurtosis used in various software packages and their differences. The observed effect of sample size and scale/shape on skewness and kurtosis is also noteworthy and may provide new insights into future research
