Statistical properties and applications of a Weibull-Kumaraswamy distribution

Abstract

The Kumaraswamy probability distribution was originally proposed by Poondi Kumaraswamy (1980) for double bounded random processes for hydrological applications. Here, we proposed a new extension of the Kumaraswamy distribution by adding one shape and one scale parameter to the Kumaraswamy distribution using the Weibull link function proposed by Tahir et al. (2015). This study has derived some expressions for its basic statistical properties such as moments, moment generating function, the characteristics function, reliability analysis, quantile function and the distribution of order statistics. Some plots of the distribution and the reliability function were generated and interpreted appropriately. The model parameters have been estimated using the method of maximum likelihood estimation. The performance of the Weibull-Kumaraswamy distribution has also been tested by some applications to two real data sets.