$${\mathcal{M}}$$ -decomposability and symmetric unimodal densities in one dimension |
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| Authors: | Nicholas Chia Junji Nakano |
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| Institution: | (1) Department of Statistical Science, School of Multidisciplinary Sciences, The Graduate University for Advanced Studies, Tokyo, Japan;(2) The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan |
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| Abstract: | 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. |
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| Keywords: |   -decomposability" target="_blank">gif" alt="$${\mathcal{M}}$$" align="middle" border="0"> -decomposability Symmetric unimodal densities Inequality Non-parametric criterion for clustering |
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