Discriminating between gamma and lognormal distributions with applications

In this paper, we discuss the use of the coefficient of skewness as a goodness-of-fit test to distinguish between the gamma and lognormal distributions. We also show the limitations of this idea. Next, we use the moments of order statistics from gamma distribution to adjust the correlation goodness-of-fit test. In addition, we calculate the power of the test based on some other alterative distributions including the lognormal distribution. Further, we show some numerical illustration. Finally, we apply the procedure developed in the paper to some real data sets.