This is more of a theoretical question. I have a response variable that is best described by the Box-Cox Power Exponential distribution, but there is no way to really "run a GLM" with this information (i.e. no BCPE "family")...should I be looking for the "next best" family and link functions for the GLM? for instance, should I use an inverse gamma family/link since it is closest to the BCPE?


  • $\begingroup$ Could you explain the basis for your assumption of this distribution? It cannot be derived validly from analyzing the response variable alone, because (if your model is any good at all) the distribution is a combination of the part of the response due to the variation in the explanatory variables along with a random component. BTW, would a "Box-Cox Power Exponential distribution" be one of the generalized Gamma distributions? $\endgroup$ – whuber Jun 3 '20 at 16:38
  • $\begingroup$ Hi @whuber thanks for the response. My basis for determining the distribution is a few days of comparing different distribution AIC's as well as the output of gamlss... I guess my misunderstanding is about the purpose of the GLM family function. I was always told (and thought) to base it off of the distribution of the response variable, ergo the foray into distribution fitting...I am not sure about your last question. Thanks $\endgroup$ – jameshgrn Jun 3 '20 at 16:46
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    $\begingroup$ The relevant distribution is the conditional distribution of the response, which you expect to vary with the explanatory variable. If it's unclear whether your "Box-Cox Power Exponential Distribution" is a generalized Gamma, could you provide a more specific description of what your distribution actually is? $\endgroup$ – whuber Jun 3 '20 at 16:50
  • $\begingroup$ @whuber this is from the "gamlss" documentation on BCPE rdocumentation.org/packages/gamlss.dist/versions/5.1-6/topics/… $\endgroup$ – jameshgrn Jun 3 '20 at 16:54
  • $\begingroup$ @whuber I am having trouble understanding the conditional distribution of the response, is this the same as normality of residuals? $\endgroup$ – jameshgrn Jun 3 '20 at 16:57

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