C23. Positive continuous responses

Topic: Underdispersion, positive responses, and quasi-likelihood · more questions on this topic
‹ Q55 C27 ›

What response support and mean–variance relationships define Gamma and inverse-Gaussian GLMs?

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Definitions/notation. Both families have support y>0, conditional mean \mu_i>0 and dispersion \phi>0: Gamma variance is \phi\mu_i^2, whereas inverse-Gaussian variance is \phi\mu_i^3. In shape–rate notation the Gamma distribution is \operatorname{Gamma}(1/\phi,1/(\phi\mu_i)); the inverse-Gaussian family is distinct from the inverse-Gamma family.