It is a generalized linear model with a linear combination of covariates related to the response via a canonical link function.
Why weibull distribution is not a glm?
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6I think you have nearly answered your own question by adding the "exponential-family" tag. The Weibull distribution is not a member of the exponential-family and hence not a glm. See wikipedia – oizin Aug 27 '18 at 06:32