The Volcano Distribution with an Application to Stock Market Returns

Abstract:

Power-law distributions have a wide range of applications including physics, economics, and biology. We derive a new family of densities with support on the real line which obeys a broken power law called the volcano distribution. An estimation procedure is also outlined. The volcano density is very flexible as it can be unbounded or bimodal. It allows for an infinite mean or an undefined mean. The complexity of this distribution calls for a novel semiparametric estimation approach which we apply to stock market returns data.