Abstract
In this paper, we will introduce the new Kumaraswamy-power series class of distributions. This new class is obtained by compounding the Kumaraswamy distribution of Kumaraswamy (1980) and the family of power series distributions. The new class contains some new double bounded distributions such as the Kumaraswamy-geometric, -Poisson, -logarithmic and -binomial, which are used widely in hydrology and related areas. In addition, the corresponding hazard rate function of the new class can be increasing, decreasing, bathtub and upside-down bathtub. Some basic properties of this class of distributions such as the moment generating function, moments and order statistics are studied. Some special members of the class are also investigated in detail. The maximum likelihood method is used for estimating the unknown parameters of the members of the new class. Finally, an application of the proposed class is illustrated using a real data set.
Keywords
- Kumaraswamy distribution
- Maximum likelihood estimation
- Power series distributions
- Uniform-power series distributions
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