Kumaraswamy’s distribution: A beta-type distribution with some tractability advantages

A two-parameter family of distributions on (0,1)(0,1) is explored which has many similarities to the beta distribution and a number of advantages in terms of tractability (it also, of course, has some disadvantages). Kumaraswamy’s distribution has its genesis in terms of uniform order statistics, and has particularly straightforward distribution and quantile functions which do not depend on special functions (and hence afford very easy random variate generation). The distribution might, therefore, have a particular role when a quantile-based approach to statistical modelling is taken, and its tractability has appeal for pedagogical uses. To date, the distribution has seen only limited use and development in the hydrological literature.