A study of generalized normal distributions

ABSTRACT

In this work, first some distributional properties of extended two-piece skew normal distributions are presented. Next we revisit the special case, that is two-piece skew normal distributions. Then two distributions related to two-piece skew normal distributions are studied. More precisely, we give some properties about generalized half normal distributions as well as a generalized Cauchy distribution. Finally, we discuss the distributions of linear combinations of two independent skew normal random variables.

KEYWORDS:

• Half-normal
• skew-Cauchy
• skew-normal
• two-piece skew normal
• uni/bimodal distribution.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E05
• 62E15
• 62E20

Acknowledgments

The authors are very grateful to the editor and the two referees for the valuable comments and suggestions that have considerably improved this work.

Additional information

Funding

Wen-Jang Huang support for this research was provided in part by the National Science Council of the Republic of China, Grant No. NSC 100-2118-M-390-002-MY2. Nan-Cheng Su support for this research was provided in part by the National Science Council of the Republic of China, Grant Nos. NSC 100-2118-M-006-002, NSC 102-2118-M-305-003.