Skew normal distribution has been introduced by Azzalini (1985) as an alternative to the normal distribution to accommodate asymmetry. Since then extensive studies have been done on applying Azzalini’s skewness mechanism to other well-known distributions, such as skew-t distribution which is more flexible and can better accommodate long tailed data than the skew normal one. Cordeiro and de Castro (2011) proposed a new class of distribution called the Kumaraswamy generalized distribution (Kw − F) which is capable of fitting skewed data that cannot be fitted well by existing distributions. Since then, the Kw −F distribution has been widely studied and various versions of generalization of this distribution family have been introduced. In this paper we introduce a new generalization of the skew-t distribution based on the Kumaraswamy generalized distribution. The new class of distribution which we call the Kumaraswamy skew-t (KwST) has the ability of fitting skewed, long and heavy tailed data and is more flexible than the skew-t distribution as it contains the skew-t distribution as a special case. Related properties of this distribution family such as mathematical properties, moments, and order statistics are discussed. The proposed distribution is applied to a real data set to illustrate the estimation procedure.
Ning, Wei; Said, Khamis K.; Basalamah, Doaa; and Gupta, Arjun K., "The Kumaraswamy Skew-t Distribution and Its Related Properties" (2017). Mathematics and Statistics Faculty Publications. 73.
Communications in Statistics - Simulation and Computation
Taylor & Francis