Modes and moments of unimodal distributions

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.