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As mentioned and explained in detail in this Math Exchange here, particularly by Peter Westfall, Kurtosis only measures "extremity of the tails", not the "peak" of the distribution which can even become more flat-topped (in that example) as the distribution exhibits higher kurtosis.

Are there any papers or works or references that provide suitable measures which capture the % of distribution that lies in a neigborhood around the mode (wlog, say mode is defined by half-sample mode)? Or, some notion of peak of a distribution?

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  • $\begingroup$ Interquartile range or related for the former? No reference needed for that. Second derivative of the (standardized) density evaluated at the mode for the latter? I haven't seen that in a reference, but it's somewhat related to Wald intervals, and Efron's empirical FDR measure. $\endgroup$ – Peter Westfall May 22 at 15:56

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