The Kumaraswamy skew-t distribution and its related properties

ABSTRACT

Skew normal distribution is an alternative distribution 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. The Kumaraswamy generalized distribution (Kw − F) is another new class of distribution which is capable of fitting skewed data that can not be fitted well by existing distributions. Such a distribution has been widely studied and various versions of generalization of this distribution family have been introduced. In this article, 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 dataset to illustrate the estimation procedure.

KEYWORDS:

• Kumaraswamy distribution
• Kumaraswamy skew-t distribution
• Maximum likelihood estimation
• Skew-t distribution

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62H10, 62H12
• Secondary 62E15

Acknowledgment

The authors are grateful to the editors and one anonymous referee for their valuable comments and suggestions that substantially improved the quality of the article.