Classification of Probability Laws by Tail Behavior

Abstract

In this article I refine Parzen's density-quantile tail exponent classification of probability laws by tail behavior by subdividing his medium-tailed class into medium-short, medium-medium, and medium-long. I give a physical interpretation of short-, medium-, and long-tailed distributions in terms of the limiting size of the extreme spacings in a random sample from the distribution. I show that this classification, by the limiting size of extreme spacings, fits nicely within the framework of my refinement of Parzen's density-quantile classification.

Key Words:

• Density quantile
• Extreme-value theory
• Extreme spacings
• Tail classification