A new generalized normal distribution: Properties and applications

Abstract

The most commonly studied generalized normal distribution is the well-known skew-normal by Azzalini. In this paper, a new generalized normal distribution is defined and studied. The distribution is unimodal and it can be skewed right or left. The relationships between the parameters and the mean, variance, skewness, and kurtosis are discussed. It is observed that the new distribution has a much wider range of skewness and kurtosis than the skew-normal distribution. The method of maximum likelihood is proposed to estimate the distribution parameters. Two real data sets are applied to illustrate the flexibility of the distribution.

Keywords:

• Beta-family
• symmetrical distribution
• hazard function
• moments
• entropy

Acknowledgments

The authors are grateful for many constructive comments and suggestions from the reviewers. These comments and suggestions have greatly improved the presentation in the paper.

Additional information

Funding

The second author gratefully acknowledges the financial support received from the U.S. Department of State, Bureau of Education and Cultural Affairs under the Fulbright Grant # PS00230565.