### 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.

Original language | English (US) |
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Pages (from-to) | 179-194 |

Number of pages | 16 |

Journal | Mathematical Geosciences |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - Feb 1 2017 |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics (miscellaneous)
- Earth and Planetary Sciences(all)

### Cite this

*Mathematical Geosciences*,

*49*(2), 179-194. https://doi.org/10.1007/s11004-016-9661-y