The natural parameter space of the exponential family dP<sub>θ</sub>（x）=C（θ）e<sup>θ’x</sup>dμ（x）,θ=（θ<sub>1</sub>,…,θ<sub>k</sub>）’ （1）is a convex se...The natural parameter space of the exponential family dP<sub>θ</sub>（x）=C（θ）e<sup>θ’x</sup>dμ（x）,θ=（θ<sub>1</sub>,…,θ<sub>k</sub>）’ （1）is a convex set in R<sup>k</sup>（see for example ref.[1]）,where μ is a σ-finite measure on β<sup>k</sup>,theσ-field of all Borel sets in R<sup>k</sup>.Is the converse true? For k=1 it is easy to see that theanswer is in the affirmative.This note considers the problem for general k.展开更多
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文摘The natural parameter space of the exponential family dP<sub>θ</sub>（x）=C（θ）e<sup>θ’x</sup>dμ（x）,θ=（θ<sub>1</sub>,…,θ<sub>k</sub>）’ （1）is a convex set in R<sup>k</sup>（see for example ref.[1]）,where μ is a σ-finite measure on β<sup>k</sup>,theσ-field of all Borel sets in R<sup>k</sup>.Is the converse true? For k=1 it is easy to see that theanswer is in the affirmative.This note considers the problem for general k.
