# Relative Abundances of Mineral Species: A Statistical Measure to Characterize Earth-like Planets Based on Earth’s Mineralogy

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## Abstract

The mineral frequency distribution of Earth’s crust provides a mineralogy-based statistical measure for characterizing Earth-like planets. It has previously been shown that this distribution conforms to a generalized inverse Gauss–Poisson large number of rare events model. However, there is no known analytic expression for the probability distribution of this model; therefore, the population probabilities do not exist in closed forms. Consequently, in this paper, the population probabilities are calculated numerically for all mineral species in Earth’s crust, including the predicted undiscovered species. These population probabilities provide an estimate of the occurrence probabilities of species in a random sample of *N* mineral species–locality pairs. These estimates are used to characterize Earth in terms of its mineralogy. The study demonstrates that Earth is mineralogically unique in the cosmos. In spite of this uniqueness, the frequency distribution of minerals from Earth can be used to quantify the extent to which another planet is Earth-like. Quantitative criteria for characterizing Earth-like planets are given. An example, involving mineral species found on Mars by the CheMin instrument during the Mars Science Laboratory mission suggests that Mars is mineralogically similar to an Earth-like planet.

## Keywords

Statistical mineralogy Mineral frequency distribution Large number of rare events distribution Mineral ecology Earth-like planets Mars mineralogy## Notes

### Acknowledgements

Two anonymous reviewers provided detailed and valuable suggestions for improving the manuscript. We received critical advice and data from Edward Grew. We gratefully acknowledge support from NASA Mars Science Laboratory Mission NNX11AP82A, as well as support from the Alfred P. Sloan Foundation (Grant Number 2013-10-01), the W. M. Keck Foundation (Grant Number 140002372), the Deep Carbon Observatory, the Carnegie Institution for Science, and an anonymous private foundation.

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