A generalized two-piece skew normal distribution and some of its properties

Abstract

In this paper, we develop a generalized version of the two-piece skew normal distribution of Kim [On a class of two-piece skew-normal distributions, Statistics 39(6) (2005), pp. 537–553] and derive explicit expressions for its distribution function and characteristic function and discuss some of its important properties. Further estimation of the parameters of the generalized distribution is carried out.

Keywords:

• method of maximum likelihood
• probability density function
• skewness
• skew normal distribution
• two-piece skew normal distribution

Acknowledgements

The authors are grateful to the Editor in Chief, Associate Editor and both the anonymous referees for their valuable comments on an earlier version of the paper. The second author is thankful to the Department of Science and Technology, Ministry of Science and Technology, New Delhi, for financial support (IF 110142).