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If this is to be based on data, rather than a fully identified joint distribution, wa simple approach is to condition on is observed values of B and the interest is if the observed counts of A tends to be higher when the count of B is higher.

As gung suggests below, if you take daily rainfall and daily hail as Bernoulli (rained or not, hailed or not, for each day), then you can deal with probability rather than counts, and there are a variety of ways to model that.

If this is to be based on data, rather than a fully identified joint distribution, a simple approach is to condition on is observed values of B and the interest is if the observed counts of A tends to be higher when the count of B is higher.

As gung suggests below, if you take daily rainfall and daily hail as Bernoulli (rained or not, hailed or not, for each day), then you can deal with probability rather than counts, and there are a variety of ways to model that. His suggestions in comments are a good way of looking at the problem (quite a bit more sophisticated than my suggestions here), and would get you closer to conditioning on estimated underlying probability per unit time rather than directly observed rate per unit time.

Here I fit a GLM with identity link (more commonly, a log link would be used, but the model here is closer to the data generating model in this particular example)

with output:

In this case, it reproduces the actual process used to create it fairly well; the true model is that $x$ was generated from a conditionally Poisson model (with mean that took two different values), and $y$ was equal to $x$ plus a 'background' Poisson process (with constant intensity).

Here I fit a GLM (in R) with identity link (more commonly, a log link would be used, but the model here is closer to the data generating model in this particular example). In this case, we fit $E(Y|X=x) = \beta_0+\beta_1 x$, which looks like a regression model, but with the GLM here the model takes account of the fact that the observations are conditionally Poisson. The command

fits the model mentioned above, with output:

In this case, the fitted model reproduces the actual process used to create it fairly well; the true model is that $x$ was generated from a conditionally Poisson model (with mean that took two different values), and $y$ was equal to $x$ plus a 'background' Poisson process (with constant intensity).

If this is to be based on data, rather than a fully identified joint distribution, what we typically (though not always) condition on is observed values of B and the interest is if the observed counts of A tends to be higher when the count of B is higher.

If this is to be based on data, rather than a fully identified joint distribution, wa simple approach is to condition on is observed values of B and the interest is if the observed counts of A tends to be higher when the count of B is higher.