Two-piece power normal distribution

Abstract

In this article, we introduce a new flexible distribution which generalizes the normal and the two-piece normal distribution. Some properties of the introduced distribution are derived, such are the cumulative distribution and the probability density function, moments, skewness, and kurtosis. The unknown parameters are estimated by the maximum likelihood method. Illustrative example of applicability and flexibility of the introduced distribution is given. At the end, we compare the flexibility of the introduced distribution and various distributions using skewness and kurtosis.

Keywords:

• Two-piece normal distribution
• skewness and kurtosis
• flexibility of distribution
• random number generator
• maximum likelihood estimator

Acknowledgments

The author thanks the Editor, the Associate Editor, and the Referees for their useful suggestions and comments which have significantly improved the article.

Disclosure statement

No potential conflict of interest was reported by the author.