%0 Journal Article
%A Khaledi, Baha-Eldin
%T Karlin’s Basic Composition Theorems and Stochastic Orderings
%J Journal of the Iranian Statistical Society
%V 13
%N 2
%U http://jirss.irstat.ir/article-1-293-en.html
%R
%D 2014
%K Likelihood ratio ordering and totally positive functions, usual stochastic ordering.,
%X 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.
%> http://jirss.irstat.ir/article-1-293-en.pdf
%P 177-186
%& 177
%!
%9
%L A-11-1-119
%+
%G eng
%@ 1726-4057
%[ 2014