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

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.