Inverse Gaussian distribution
Topic of Underdispersion, positive responses, and quasi-likelihood, part of Generalised linear models
Inverse Gaussian distribution
| Type | Topic |
| Taught in | Underdispersion, positive responses, and quasi-likelihood |
| Part | Generalised linear models |
A distribution on (0,\infty) whose variance is proportional to the cube of its mean. In a GLM its canonical link is \mu^{-2}, the inverse quadratic, which needs the linear predictor to stay positive.
In Underdispersion, positive responses, and quasi-likelihood
That separation is what Huang and Rathouz (2017) give in general. It is why families and links can be mixed, and why a worse AIC for the inverse quadratic is a statement about the link, not a mystery of the inverse Gaussian. Other positive families exist and are not in the default glm list: inverse gamma, lognormal, Weibull with the second parameter fixed. A custom family needs a log-likelihood, or, as the next section shows, sometimes only a mean and a variance.
Used in
See also
Variance · Generalised linear model · Canonical link · Linear predictor · Variance function · Quasi-score and quasi-likelihood · Bids for a bankrupt firm · Positive continuous responses