Abstract
Let X1, ..., Xn be i.i.d. random variables with common distribution an element of a linear one-parameter exponential family[Figure not available: see fulltext.] indexed by a natural parameter θ. It is proved that the distribution of {Mathematical expression} is an element of F, for all θ∈Θ and n=1, 2, ... if and only if F is a family of scale transformed Poisson distributions.
Original language | English |
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Pages (from-to) | 391-394 |
Number of pages | 4 |
Journal | Metrika |
Volume | 32 |
Issue number | 1 |
DOIs | |
State | Published - Dec 1985 |
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty