Annals of the Institute of Statistical Mathematics

, Volume 39, Issue 1, pp 407-415

First online:

Modes and moments of unimodal distributions

  • Ken-iti SatoAffiliated withNagoya University

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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.

Key words and phrases

Unimodal distribution mode moment