A Note on the Reparametrization of an Exponential Family

Open Access
Publisher Website
Google Scholar
Abstract
Distributions considered in statistics (see [l] or [5]). In this note we restrict attention to one-dimensional exponential families. For p, a a-finite measure on R, we define a = inf {x:p([x, x+E)) > 0 for all E > 0) and b = sup { X : ~ ( ( X--E, x]) > 0 for all E > O}. If a and b are finite, we define A@) by A@) = [a, b]. If a or b are infinite, we use open or half-open intervals. The parameter space of p,a(p), is defined by n(p) = {w : 0 < j emx dp(x) = w(o) < + a}.

This publication has 0 references indexed in Scilit: