A novel skewed generalized normal distribution: properties, statistical inference, and its applications

Abstract

In this paper, a novel skewed generalized normal distribution (NSGN), which encompasses several well-known distributions, is a two-component mixture model based on the generalized normal distribution. The NSGN distribution offers flexibility in modeling skewed data characterized by high kurtosis and strong skewness, making it highly applicable in finance, medicine, and engineering. The primary characteristics and properties of this new distribution are introduced, and the explicit expressions for the moments of order statistics are provided using recursive relations. The maximum likelihood estimation based on a profile likelihood approach, L-moments estimation, and a two-step estimation method combining Bayesian posterior maximum estimation with moment estimates are presented to estimate the four parameters of NSGN distribution. A simulation study compares the performance of these methods across different sample sizes and different parameters. The appropriateness of the proposed distribution has been tested by comparing it with several skewed distributions. Additionally, applications to real datasets showcase the beneficial properties of the NSGN for applied statistical research.

Keywords:

• L-moments estimation
• Order statistics
• Profile likelihood approach
• Simulation study
• Skewed generalized normal distribution

MATHEMATICAL SUBJECT CLASSIFICATION:

• Primary 62E15
• Secondary 62P20

Disclosure statement

No potential conflict of interest was reported by the author(s).