Some asymptotic inferential aspects of the Kumaraswamy distribution

The Kumaraswamy distribution is doubly limited, continuous, very flexible, and is widely applied in hydrology and related areas. Recently, several families of distributions based on this distribution have emerged. To make a contribution regarding some asymptotic aspects related to the inferential analysis, we derived an analytic expression of order n(-1/2), where n is the sample size, for the skewness coefficient of the distribution of the maximum likelihood estimators of the parameters of the Kumaraswamy distribution. A simulation study and an application are presented to illustrate that, when the sample size is small, the likelihood inferences may not be reliable. We also obtain Bartlett correction factors for the likelihood ratio statistic as well as the results of the bootstrap likelihood ratio test and bootstrap Bartlett correction and present a Monte Carlo simulation study to compare the rejection rates of the tests in question.