RT - Journal Article
T1 - Karlin’s Basic Composition Theorems and Stochastic Orderings
JF - JIRSS
YR - 2014
JO - JIRSS
VO - 13
IS - 2
UR - http://jirss.irstat.ir/article-1-293-fa.html
SP - 177
EP - 186
K1 - Likelihood ratio ordering and totally positive functions
K1 - usual stochastic ordering.
AB - 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.
LA eng
UL http://jirss.irstat.ir/article-1-293-fa.html
M3
ER -