Exponential dispersion model

Exponential dispersion models are statistical models in which the probability distribution is of a special form.[1][2] This class of models represents a generalisation of the exponential family of models which themselves play an important role in statistical theory because they have a special structure which enables deductions to be made about appropriate statistical inference.

Definition

Exponential dispersion models are a generalisation of the natural exponential family: these have a probability density function which, for a multivariate model, can be written as

where the parameter has the same dimension as the observation variable . The generalisation includes an extra scalar "index parameter", , and has density function of the form[1]

The terminology "dispersion parameter" is used for , while is the "natural parameter" (also known as "canonical parameter").

References

  1. 1 2 Jørgensen, B. (1987). Exponential dispersion models (with discussion). Journal of the Royal Statistical Society, Series B, 49 (2), 127162.
  2. Marriott, P. (2005) "Local Mixtures and Exponential Dispersion Models" pdf
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