Lognormal distribution
Topic of Underdispersion, positive responses, and quasi-likelihood, part of Generalised linear models
Lognormal distribution
| Type | Topic |
| Taught in | Underdispersion, positive responses, and quasi-likelihood |
| Part | Generalised linear models |
| Questions using it | 3 |
The law of e^Z when Z is normal. Its variance is (e^{\sigma^2}-1)\mu^2, proportional to the square of its mean as for the gamma, so for positive responses a lognormal model and a gamma GLM with log link often agree.
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
- Taught in Underdispersion, positive responses, and quasi-likelihood
- Also used in Conjugate analysis for normal models
- Questions that use it (3) — Q28 · Q45 (answer) · Question 7
- All 6 questions on Underdispersion, positive responses, and quasi-likelihood
See also
Variance · Gamma regression · Log link · Quasi-score and quasi-likelihood · Bids for a bankrupt firm · Positive continuous responses · Quasi-likelihood · Leaf-blotch data