On the linear exponential family
Published online by Cambridge University Press: 24 October 2008
Extract
In this paper we give a characterization theorem for a subclass of the exponential family whose probability density function is given by
where a(x) ≥ 0, f(ω) = ∫a(x) exp (ωx) dx and ωx is to be interpreted as a scalar product. The random variable X may be an s-vector. In that case ω will also be an s-vector. For obvious reasons we will call (1) as the linear exponential family. It is easy to verify that the moment generating function (m.g.f.) of (1) is given by
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 64 , Issue 2 , April 1968 , pp. 481 - 483
- Copyright
- Copyright © Cambridge Philosophical Society 1968
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