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Products of random variables and star‐shaped ordering
Author(s) -
Rivest LouisPaul
Publication year - 1982
Publication title -
canadian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.804
H-Index - 51
eISSN - 1708-945X
pISSN - 0319-5724
DOI - 10.2307/3556185
Subject(s) - star (game theory) , random variable , mathematics , combinatorics , monotone polygon , property (philosophy) , statistics , mathematical analysis , geometry , philosophy , epistemology
It is shown that if V 1 and V 2 are two positive random variables such that V 1 is “star‐shaped” with respect to V 2 , then for any random variable X with a distribution F(x) such that F(ax) has the monotone likelihood‐ratio property, XV 1 is star‐shaped with respect to XV 2 . This result is then used to prove that the stable laws are star‐shaped ordered.