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Bounds of modes and unimodal processes with independent increments
Published online by Cambridge University Press: 22 January 2016
Extract
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]).
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1986
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