Reference analysis is one of the most successful general methods to derive noninformative prior distributions. In practice, however, reference priors are often difficult to obtain. Recently developed theory for conditionally reducible natural exponential families identifies an attractive...

If I=(I1,...,Id) is a random variable on [0,[infinity])d with distribution [mu](d[lambda]1,...,d[lambda]d), the mixed Poisson distribution MP([mu]) on is the distribution of (N1(I1),...,Nd(Id)) where N1,...,Nd are ordinary independent Poisson processes which are also independent of I. The paper...

Let p>1. If Y=(Y(t))t[greater-or-equal, slanted]0 is a positive Lévy process and if T is an exponential standard random variable independent of Y, we prove that Y(T) and Y(T)/Tp are independent if and only if Y(t) has a certain drifted stable distribution with parameter 1/p.