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 essential 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”. For a discrete distribution, the peakedness index is defined as the ratio of the maximum (peak) probability to its discrete informity; for a continuous distribution, it is defined as the ratio of the maximum (peak) density to its continuous informity, where “informity” is a concept introduced in the recently developed theory of informity. The peakedness indices for ten well-known distributions are presented and compared with the traditional kurtosis measure.