A New Index for Quantifying the Peakedness of a Probability Distribution

Peakedness is an important characteristic of probability distributions, and an effective method for quantifying peakedness is crucial for statistical modeling and comparing different probability distributions in many practical applications. However, there has long been a misconception that kurtosis (or excess kurtosis) serves as a measure of peakedness. In this paper, we propose a new measure for quantifying peakedness, named the “peakedness index”. The proposed index is defined as the ratio of the maximum density (or peak density) of the distribution to its continuous informity, where “continuous informity” is a concept from the newly developed theory of informity. The peakedness indices for nine well-known distributions are presented and compared to the traditional kurtosis measure.