Annals of the Institute of Statistical Mathematics

, Volume 39, Issue 1, pp 407–415

Modes and moments of unimodal distributions

  • Ken-iti Sato

DOI: 10.1007/BF02491478

Cite this article as:
Sato, Ki. Ann Inst Stat Math (1987) 39: 407. doi:10.1007/BF02491478


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|≦Apβp1/p (p>0) and |a−m|≦Bpγp1/p (p≧1) wherem is the mean. the results follow from discussion of more general moments.

Key words and phrases

Unimodal distributionmodemoment

Copyright information

© Kluwer Academic Publishers 1987

Authors and Affiliations

  • Ken-iti Sato
    • 1
  1. 1.Nagoya UniversityNagoyaJapan