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On the linear exponential family

Published online by Cambridge University Press:  24 October 2008

J. K. Wani
J. K. Wani
Affiliation:
Saint Mary's University, Halifax
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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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References

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