Mean Absolute Deviation (About Mean) Metric for Kurtosis

In this paper, we introduce a MAD (about mean) alternative metric to classical kurtosis. Using the formula for mean absolute deviation, we identify two special points and construct the corresponding distributions with these reference points as their means. The proposed alternative is computed from mean absolute deviations for these distributions. These measures are bounded, require only the existence of first-order moments, and are easy to interpret. We illustrate the computation of these measures for several well-known distributions.