Exponential Families

David J. Olive
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David J. Olive: Southern Illinois University, Department of Mathematics

Chapter Chapter 3 in Statistical Theory and Inference, 2014, pp 81-99 from Springer

Abstract: Abstract Suppose the data is a random sample from some parametric brand name distribution with parameters θ $$\boldsymbol{\theta }$$ . This brand name distribution comes from a family of distributions parameterized by θ ∈ Θ $$\boldsymbol{\theta } \in \varTheta$$ . Each different value of θ $$\boldsymbol{\theta }$$ in the parameter space Θ gives a distribution that is a member of the family of distributions. Often the brand name family of distributions is from an exponential family.

Keywords: Regular Exponential Family; Family Brand Name; Natural Parameter Space; Inverted Gamma; Burr Type (search for similar items in EconPapers)
Date: 2014
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DOI: 10.1007/978-3-319-04972-4_3

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