Modes and moments of unimodal distributions
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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 phrasesUnimodal distribution mode moment
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- Hardy, G. H., Littlewood, J. E. and Pólya, G. (1934).Inequalities. Cambridge University Press, Cambridge.Google Scholar