Timeline for Capped binomial random variables
Current License: CC BY-SA 3.0
2 events
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| Mar 2, 2013 at 15:36 | comment | added | Lutz Mattner | $Y$ is smaller than $X$ in the convex order, by bounding from above any convex function on $[0,1]$ by the secant line passing through the points $(0,g(0))$ and $(1,g(1))$; this is Lemma 1 in cardinal's answer. And yes, convex order inequalities between between laws on the line (or a measurable vector space over the reals) "can be multiplied" with respect to convolution; this is Lemma 2 from above formulated in its natural generality. Books treating such things include \textit{Stochastic Orders} by Shaked and Shantikhumar (2007) and \texit{Comparison Methods ...} by Müller and Stoyan (2002). | |
| Apr 15, 2012 at 17:27 | history | answered | mike | CC BY-SA 3.0 |