How many strong earthquakes will there be tomorrow?

In this note, we study the distribution of earthquake numbers in both worldwide and regional catalogs: in the Global Centroid Moment Tensor catalog, from 1980 to 2019 for magnitudes Mw 5. 5+ and 6.5+ in the first case, and in the Italian instrumental catalog from 1960 to 2021 for magnitudes Mw 4.0+ and 5.5+ in the second case. A subset of the global catalog is also used to study the Japanese region. We will focus our attention on short-term time windows of 1, 7, and 30 days, which have been poorly explored in previous studies. We model the earthquake numbers using two discrete probability distributions, i.e., Poisson and Negative Binomial. Using the classical chi-squared statistical test, we found that the Poisson distribution, widely used in seismological studies, is always rejected when tested against observations, while the Negative Binomial distribution cannot be disproved for magnitudes Mw 6.5+ in all time windows of the global catalog. However, if we consider the Japanese or the Italian regions, it cannot be proven that the Negative Binomial distribution performs better than the Poisson distribution using the chi-squared test. When instead we compared the performances of the two distributions using the Akaike Information Criterion, we found that the Negative Binomial distribution always performs better than the Poisson one. The results of this study suggest that the Negative Binomial distribution, largely ignored in seismological studies, should replace the Poisson distribution in modeling the number of earthquakes.