Confusion of rate and shape

I may be wrong here, but according to the [Wikipedia page](https://en.wikipedia.org/wiki/Inverse-gamma_distribution), if X is gamma-distributed with shape _a_ and rate _b_, then 1/X is IG-distributed with shape _a_ and rate 1/_b_ (and thus scale _b_). The converse holds true as well. But it seems to me that in your function dinvgamma, for example, the rate of the IG distribution is used directly as the rate in the function stats::dgamma, without first taking the reciprocal.

Start with the dinvgamma function and compare its rate handling with the inverse-gamma relationship described in the linked Wikipedia page and the parameterization used by stats::dgamma. Done means the rate/scale conversion is consistent in dinvgamma and the related distribution behavior is verified.

Written by the indexing model from the issue text.