Credibility and relative exchangeability

We define relative exchangeability by saying that n random vectors x1, ... , x n all of the same dimension, are exchangeable relative to a random vector u if has the same distribution for all permutations (i 1, ... ,in ) of (1, ..., n). A theorem is given that simplifies the construction of credibility estimators under relative exchangeability. We show that if we have a sequence of real random vectors of same dimension such that xl, ..., X n are exchangeable relative to u for all n, there exists a σ-field such that u, x1, x2, ... are conditionally independent and the x i 's equi-distributed given .