Alfredo Quiroz-Ruiz

Comparative Performance of Four Single Extreme Outlier Discordancy Tests from Monte Carlo Simulations

Using highly precise and accurate Monte Carlo simulations of 20,000,000 replications and 102 independent simulation experiments with extremely low simulation errors and total uncertainties, we evaluated the performance of four single outlier discordancy tests (Grubbs test N2, Dixon test N8, skewness test N14, and kurtosis test N15) for normal samples of sizes 5 to 20. Statistical contaminations of a single observation resulting from parameters called δ from ±0.1 up to ±20 for modeling the slippage of central tendency or ε from ±1.1 up to ±200 for slippage of dispersion, as well as no contamination (δ = 0 and ε = ±1), were simulated. Because of the use of precise and accurate random and normally distributed simulated data, very large replications, and a large number of independent experiments, this paper presents a novel approach for precise and accurate estimations of power functions of four popular discordancy tests and, therefore, should not be considered as a simple simulation exercise unrelated to probability and statistics. From both criteria of the Power of Test proposed by Hayes and Kinsella and the Test Performance Criterion of Barnett and Lewis, Dixon test N8 performs less well than the other three tests. The overall performance of these four tests could be summarized as N2≅N15 > N14 > N8.

Log-ratio transformed major element based multidimensional classification for altered High-Mg igneous rocks

A new multidimensional classification scheme consistent with the chemical classification of the International Union of Geological Sciences (IUGS) is proposed for the nomenclature of High-Mg altered rocks. Our procedure is based on an extensive database of major element (SiO2, TiO2, Al2O3, Fe2O3t, MnO, MgO, CaO, Na2O, K2O, and P2O5) compositions of a total of 33868 (920 High-Mg and 32948 “Common”) relatively fresh igneous rock samples. The database consisting of these multinormally distributed samples in terms of their isometric log-ratios was used to propose a set of 11 discriminant functions and 6 diagrams to facilitate High-Mg rock classification. The multinormality required by linear discriminant and canonical analysis was ascertained by a new computer program DOMuDaF. One multidimensional function can distinguish the High-Mg and Common igneous rocks with high percent success values of about 86.4% and 98.9%, respectively. Similarly, from 10 discriminant functions the High-Mg rocks can also be classified as one of the four rock types (komatiite, meimechite, picrite, and boninite), with high success values of about 88% to 100%. Satisfactory functioning of this new classification scheme was confirmed by seven independent tests. Five further case studies involving application to highly altered rocks illustrate the usefulness of our proposal. A computer program HMgClaMSys was written to efficiently apply the proposed classification scheme, which will be available for online processing of High-Mg igneous rock compositional data. Monte Carlo simulation modelling and mass-balance computations confirmed the robustness of our classification with respect to analytical errors and post-emplacement compositional changes. This article is protected by copyright. All rights reserved.