Bimodal skew-symmetric normal distribution

ABSTRACT

We introduce a new parsimonious bimodal distribution, referred to as the bimodal skew-symmetric Normal (BSSN) distribution, which is potentially effective in capturing bimodality, excess kurtosis, and skewness. Explicit expressions for the moment-generating function, mean, variance, skewness, and excess kurtosis were derived. The shape properties of the proposed distribution were investigated in regard to skewness, kurtosis, and bimodality. Maximum likelihood estimation was considered and an expression for the observed information matrix was provided. Illustrative examples using medical and financial data as well as simulated data from a mixture of normal distributions were worked.

KEYWORDS:

• Bimodality parameter
• Financial data
• Flexible skew-symmetric distributions
• Gene expression bimodality
• Mixture of normal distributions
• Plasma lipid levels of cardiovascular risk

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E99
• 62E15
• 62F10

Funding

The second author research was funded by the Summer Research Grant Program of the Faculty of Business and Economics, UAE University.

Funding

The second author research was funded by the Summer Research Grant Program of the Faculty of Business and Economics, UAE University.