Convolution of a symmetric log-concave distribution and a symmetric bimodal distribution can have any number of modes - Inria - Institut national de recherche en sciences et technologies du numérique
Article Dans Une Revue Statistics and Probability Letters Année : 2021

Convolution of a symmetric log-concave distribution and a symmetric bimodal distribution can have any number of modes

Charles Arnal

Résumé

In this note, we show that the convolution of a discrete symmetric log-concave distribution and a discrete symmetric bimodal distribution can have any strictly positive number of modes. A similar result is proved for smooth distributions, which contradicts the main statement in Hou et al. (2017).
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hal-04471575 , version 1 (22-07-2024)

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Charles Arnal. Convolution of a symmetric log-concave distribution and a symmetric bimodal distribution can have any number of modes. Statistics and Probability Letters, 2021, 173, pp.109082. ⟨10.1016/j.spl.2021.109082⟩. ⟨hal-04471575⟩
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