M{mathcal{M}} -decomposability and symmetric unimodal densities in one dimension

摘要

In this paper, we introduce the notion of -decomposability of probability density functions in one dimension. Using -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 -decomposability can be used as a non-parametric criterion for mode-finding and cluster analysis. Keywords -decomposability - Symmetric unimodal densities - Inequality - Non-parametric criterion for clustering