A study of geometric and statistical curvatures for the skew-normal family of distributions

ABSTRACT

With special reference to the family of skew-normal distributions, we consider geometric curvature of a probability density function as a means to define and identify rare or catastrophic events—a phenomenon common in studying the financial instruments. Further, we study the statistical curvature properties of this family of distributions and discuss the sample size issue, to assess, to what extent the linear and likelihood-based inference of exponential family of distribution can be applicable for the skew-normal family.

KEYWORDS:

• Choosing level of significance
• Exponential family of distributions
• Geometric curvature
• Skew-normal distribution
• Statistical curvature

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62F03, 62F05, 62F10
• Secondary 62E17

Acknowledgment

The authors wish to thank an anonymous referee for his/her critical comments that helped improve this article.