CDF of negative binomial with mu and alpha in python

Question content

I have some count data, somewhat similar to a Poisson distribution, but too spread out. I fitted a negative binomial glm model in python using statsmodels and selected the alpha value (i.e. the dispersion parameter). I then apply the model to the test set to make some predictions. I now want to compute the cumulative distribution function that calculates the probability of a random variable X<=9 given the output prediction mu (i.e. 7.8) and a predetermined alpha value (i.e. 0.2).

scipy documentation (https://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.nbinom.html) suggests that I can use nbinom.cdf(k, n, p) but when I only How do I get the values ​​of n and p when mu and alpha are given?

Correct answer

p and n are related to alpha and mu, the relationship is given in the document you provided:

sigma_squared = mu + alpha * mu**2
p = mu / sigma_squared
n = mu**2 / (sigma_squared - mu)

This is equivalent to:

p = 1 / (1 + alpha * mu)
n = 1 / alpha

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