How to choose the distribution and parameters for continuous probability density functions in naive Bayes using maximum likelihood?

Let's assume I want to train a binary naive Bayes classifier, with classes $y_0, y_1$ and $n$-dimensional data. For this one needs to calculate the conditional probabilities $P(x_i | y_j)$ for all pairs $i,j$.

When the distribution is discrete it's pretty straightforward, but let's assume I need to fit a continuous probability density function. Suppose I consider Gaussian and Poisson distributions, and would like to choose the more probable (use the ML principle). How do I choose which distribution is a better fit and what the parameters ($\lambda, \mu, \sigma)$ for those distributions should be?

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