Inconsistency between poisson and negativebinomial in glm

Description

Hi

I am working with the negativebinomial distribution for GLM. I have done one test which is finding the poisson distribution results. Here is the first test:

In this case they are both giving the same result, 16.40,17.18 ...

If I change the lambda_ parameter I have again the same result.

The problem is when lambda_search=True. In this case the optimal lambda_ parameter is totally different. I get 0.05204 for the negativebinomail and 41.008 for poisson. I think it is a bug they should be the same and the prediction as well?
Here is the code:

Thank you

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jean charles

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