Convexity of the bounds induced by Markov's inequality
X is a nonnegative random variable such that EXt < [infinity] for 0<= t < [lambda] <= [infinity]. The (l-[epsilon]) quantile of the distribution of X is bounded above by [[epsilon]-1 EXt]1[+45 degree rule]t. We show that there exist positive [epsilon]1 >= [epsilon]2 such that for all 0 <[epsilon]<=[epsilon]1 the function g(t) = [[epsilon]-1EXt]1[+45 degree rule]t is log-convex in [0, c] and such that for all 0 < [epsilon] <= [epsilon]2 the function log g(t) is nonincreasing in [0, c].
Year of publication: |
1973
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Authors: | Neuts, Marcel F. ; Wolfson, David B. |
Published in: |
Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 1.1973, 2, p. 145-149
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Publisher: |
Elsevier |
Saved in:
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