M-decomposability and symmetric unimodal densities in one dimension

摘要

In this paper, we introduce the notion of M-decomposability of probability density functions in one dimension. Using M-decomposability, we derive an inequality that applies to all symmetric unimodal densities. Our inequality involves only the standard deviation of the densities concerned. The concept of M-decomposability can be used as a non-parametric criterion for mode-finding and cluster analysis.