The principle of maximum entropy and the probability-weighted moments for estimating the parameters of the Kumaraswamy distribution

Since Shannon's formulation of the entropy theory in 1940 and Jaynes' discovery of the principle of maximum entropy (POME) in 1950, entropy applications have proliferated across a wide range of different research areas including hydrological and environmental sciences. In addition to POME, the method of probability-weighted moments (PWM), was introduced and recommended as an alternative to classical moments. The PWM is thought to be less impacted by sampling variability and be more efficient at obtaining robust parameter estimates. To enhance the PWM, self-determined probability-weighted moments was introduced by (Haktanir 1997). In this article, we estimate the parameters of Kumaraswamy distribution using the previously mentioned methods. These methods are compared to two older methods, the maximum likelihood and the conventional method of moments techniques using Monte Carlo simulations. A numerical example based on real data is presented to illustrate the implementation of the proposed procedures.