Is the Diameter of Herschel Crater, Mimas, an Outlier? A Mathematical Framework for Analyzing Planetary Feature Size‐Frequency Distribution Anomalies

Many features on planetary bodies follow a distinct size-frequency distribution (SFD), and there are practically always outliers. In impact crater studies, that SFD can be approximated with a power-law, and the nature of power-laws is there are often lone, singular largest features. An open question is whether these largest features are truly anomalous, or whether they emerge as a statistical feature of a large number of finite samples drawn from stochastic probability distributions, with significant implications for the population that formed them. Here, this question is explored by testing Mimas' largest crater, Herschel. The framework developed answers the question with two main tests, and both show Herschel is not an outlier. This is applied to other planetary bodies, where the null hypothesis is still not rejected. The framework developed is agnostic toward the probability distribution used and can be applied to many other features in planetary science.