I should probably point out that I am not writing as an expert on earthquakes in this blog but rather as a "student" of them. The expert speaks for a known science. The student is in search of knowledge while for the expert the facts have already been proven.
It is not at all certain that the probability distribution associated with earthquakes is a Poisson distribution. It seems to fit the observations with a similar peak and trailing edge. The same could be said about a binomial distribution. Even if it is a Poisson distribution there is no guarantee that the total number of earthquakes is constant over time. One point in favor of a Poisson distribution is that whole numbers are involved and the number of events is never negative.
And, I am approaching the limit of what I know or can surmise about earthquakes. I did not know about the peak in magnitude when I started. So I am still learning. The Poisson distribution involves multiplicities but the probability involved may be that something will not happen.
So to avoid babbling I will probably have to take a little more time to think about what I am doing before making new posts.