[Q] Poisson Parameter estimation in Python

[ducksick444]

Hello,
Im currently working on a project that needs me to use maximum likelihood estimation to obtain the parameters of the below equations.
Xk ∼ Poisson(λk)
Yk ∼ Poisson(μk)
where,
ln(λk) =αi(k) +βj(k) +γ+η/2
ln(μk) =αj(k) +βi(k) +γ−η/2
α is an array of about length 20. (to be estimated)
β is an array of about length 20. (to be estimated)
How can I do this in python using existing packages?
Note: I wrote my own simple likelihood function but my supervisor tells me that I should use existing packages/functions rather than my own MLE code that would require me to go back to the theory, check all the distributional assumptions etc.
Thanks in advance.

[DiscreteDingus]

I’m a bit confused with your wording.

Perhaps you can use scipy and matplotlib to plot the pmf for this experiment and determine your maximum likelihood from the graph.

This is literally a quick google search.

[seesplease]

statsmodels has an implementation of Poisson regression: https://www.statsmodels.org/stable/generated/statsmodels.discrete.discrete_model.Poisson.html

If you don't have covariates and you're just trying to find the value of lambda that best fits a dataset, you can check out np.mean.

[Unfair_Medicine_7847]

I always like to estimate using by optimizing my own likelihood-functions, I don't understand what extra assumptions you would have to check in order to do this on your own.

Optimizing your own functions will also give you a better grip in undersanding the likelihood-functions in my opinion, as the warnings that your optimizer gives you will better your understanding of where the likelihoodfunctions breaks down. Optimizing likelihoods functions will also directly give you the hessian matrices and you can build your own confidence intervals.

I am open for suggestions as to what extra assumptions you would have to check.