What is the impact of log concave density for light tailed distribution? How it could be substantiated with real time example?
Most of the books and research papers highlights that a distribution with a log-concave density f is necessarily light-tailed. In contrast, f is log-convex for heavy tails .
What is the necessity of log concave/ convex for tail distributions?
For example, Gamma distribution with shape > 1 is light tailed and <1 is heavy tailed so my question is What would be the impact of heavy and light tailed in case of gamma distribution? Which part of inference would change due to heavy and light?
