The exponential family of probability distributions generated by Ơ-finite measures Public Deposited

http://ir.library.oregonstate.edu/concern/graduate_thesis_or_dissertations/2z10wv39z

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  • The exponential family of probability distributions is obtained from σ-finite measures on the real line. We choose the parameter space to be one-dimensional and the exponent to be linear. Relationships between the measure, its spectrum, and the parameter space are examined, moments of the exponential family are studied, and the nature of a mapping of the parameter space into the spectrum is discussed. Examples of the many distributions belonging to the exponential family are given, including the binomial, Poisson, and normal with known variance. Finally, atomic probability distributions are considered, and a characterization of a certain subclass of these distributions is given.
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