A new generalized Balakrishnan type skewed–normal distribution: properties and associated inference

ABSTRACT

It is also shown that our proposed skew-normal model subsumes many other well-known skew-normal model that exists in the literature. Recent work on a new two-parameter generalized skew-normal model has received a lot of attention. This paper presents a new generalized Balakrishnan type skew–normal distribution by introducing two shape parameters. We also provide some useful results for this new generalization. It is also shown that our proposed skew–normal model subsumes the original Balakrishnan skew–normal model (2002) as well as other well–known skew–normal models as special cases. The resulting flexible model can be expected to fit a wider variety of data structures than either of the models involving a single skewing mechanism. For illustrative purposes, a famed data set on IQ scores has been used to exhibit the efficacy of the proposed model.

KEYWORDS:

• Balakrishnan skew–normal distribution
• maximum likelihood
• skewing parameter.

MATHEMATICS SUBJECT CLASSIFICATION:

• 60E
• 62F

Acknowledgments

The authors are grateful to anonymous referee(s) for making valuable comments and suggestions on an earlier version of this paper which improved our paper.