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Bounds of modes and unimodal processes with independent increments

Published online by Cambridge University Press:  22 January 2016

Ken-Iti Sato
Ken-Iti Sato*
Affiliation:
Department of Mathematics, College of General Education, Xagoya University, Nagoya, Japan
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A probability measure μ is called unimodal if there is a point α such that the distribution function of μ is convex on (− ∞, α) and concave on (α, ∞). The point α is called a mode of μ. When μ is unimodal, the mode of μ is not always unique; the set of modes is a one point set or a closed interval. If μ is a unimodal distribution with finite variance, Johnson and Rogers [6] give a bound

where m and v are mean and variance of μ (see also [11]).

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 104 , December 1986 , pp. 29 - 42
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1986

References

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