Convolution of a symmetric log-concave distribution and a symmetric bimodal distribution can have any number of modes
Statistics & Probability Letters, 2021, vol. 173, issue C
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).
Keywords: Modes; Convolution; Log-concavity (search for similar items in EconPapers)
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