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I have a dataset containing counts (values from 0 to 30) and different covariates. This is what the distribution of the count data looks like:

enter image description here

After fitting a gamlss boosting model in R (with the function gamboostLSS, zinb distribution) I plotted the probability distribution of one observed subject (out of my dataset) to get a first impression of the model. However, the probability distribution doesn't look at all like the expected distribution (zero-inflated negativ binomial, see plot above).

probability distribution of an observed subject

I plotted several probability distributions for different observed subjects, but they all look like the distribution shown above. After checking the three parameters of the zinb model for the observed subjects, I figured that the overdispersion parameter is quite small, which is the reason for the unexpected probability distribution. What could be the reason the overdispersion parameter is so small / way smaller than expected? Does the plot indicate that my model is bad? To find out the optimal hyperparameters I used a 10-fold crossvalidation. Thank you in advance for your help!

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