Journal of the Iranian Statistical Society پژوهشنامه انجمن آمار ایران JIRSS Basic Sciences http://jirss.irstat.ir 1 admin 1726-4057 2538-189X 8 10.29252/jirss 14 1726-4057 13 en jalali 1393 9 1 gregorian 2014 12 1 13 2 online 1 fulltext
en Karlin’s Basic Composition Theorems and Stochastic Orderings Suppose λ,x,ζ traverse the ordered sets Λ, X and Z, respectively and consider the functions f(λ,x,ζ) and g(λ,ζ) satisfying the following conditions, (a) f(λ,x,ζ) > 0 and f is TP2 in each pairs of variables when the third variable is held ﬁxed and (b) g(λ,ζ) is TP2. Then the function h(λ,x) =∫Z f(λ,x,ζ)g(λ,ζ)dµ(ζ), deﬁned on Λ×X is TP2 in (λ,x). The aim of this note is to use a new stochastic ordering argument to prove the above result and simplify it’s proof given by Karlin (1968). We also prove some other new versions of this result. Likelihood ratio ordering and totally positive functions, usual stochastic ordering. 177 186 http://jirss.irstat.ir/browse.php?a_code=A-11-1-119&slc_lang=en&sid=1 Baha-Eldin Khaledi bkhaledi@hotmail.com `1003194753284600741` 1003194753284600741 Yes