Summary
For a unimodal distribution relations of its modea with its absolute momentβp and central absolute momentγp of orderp are considered. The best constantAp andBp are given for the inequalities |a|≦Apβ 1/ p p (p>0) and |a−m|≦Bpγ 1/ p p (p≧1) wherem is the mean. the results follow from discussion of more general moments.
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Sato, Ki. Modes and moments of unimodal distributions. Ann Inst Stat Math 39, 407–415 (1987). https://doi.org/10.1007/BF02491478
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DOI: https://doi.org/10.1007/BF02491478