Modes and moments of unimodal distributions

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Summary

For a unimodal distribution relations of its modea with its absolute momentβ p and central absolute momentγ p of orderp are considered. The best constantA p andB p are given for the inequalities |a|≦A p β p 1/p (p>0) and |a−m|≦B p γ p 1/p (p≧1) wherem is the mean. the results follow from discussion of more general moments.