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Products of random variables and star-shaped ordering |
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| Authors: | Louis-Paul Rivest |
| Abstract: | It is shown that if V1 and V2 are two positive random variables such that V1 is “star-shaped” with respect to V2, then for any random variable X with a distribution F(x) such that F(ax) has the monotone likelihood-ratio property, XV1 is star-shaped with respect to XV2. This result is then used to prove that the stable laws are star-shaped ordered. |
| Keywords: | Total positivity stable law monotone likelihood ratio |