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The Poisson extreme stable Tweedie family: a novel count distribution

Abstract Number:

3188

Submission Type:

Contributed Abstract

Contributed Abstract Type:

Paper

Participants:

Frederick Townes (1)

Institutions:

(1) Carnegie Mellon University, Pittsburgh, PA

First Author:

Will Townes
Carnegie Mellon University

Presenting Author:

Will Townes
Carnegie Mellon University

Abstract Text:

The compound Poisson-Tweedie family is suitable for modeling a wide range of count (discrete, nonnegative) data. The Poisson rate is assigned a nonnegative-valued Tweedie mixing distribution, which is indexed by a real-valued shape parameter, "p". For example, gamma distributions are Tweedie with p=2, and the corresponding Poisson-Tweedie is the negative binomial. Surprisingly, the Hermite distribution is analogous to mixing a Poisson with a Gaussian (p=0) and can be derived using generating functions, despite the mismatch of support, so long as constraints on the natural parameter are satisfied. The extreme stable Tweedie distributions (p<0) have sub-exponential left tails, with the right tail following a power law with exponential cutoff. They are adjacent to Gaussians and are similarly real-valued. For this reason they have been excluded from consideration in Poisson-Tweedie models. We prove that the Poisson extreme stable Tweedie (PEST) family exists and explore its properties. We illustrate sampling from PEST distributions as well as estimation and inference for PEST regression models.

Keywords:

Sponsors:

Section on Bayesian Statistical Science

Tracks:

Miscellaneous

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