Selection of Appropriate Probability Distributions for Rock Analysis using Laser-induced Breakdown Spectroscopy

In this work, an attempt is made to fit and identify the most appropriate probability distribution(s) for the analysis of seventeen rock samples including diorite, gypsum, marble, basalt, sandstone, limestone, apatite, slate, dolomite, granite-II, schist, gneiss, amphibolite, hematitle, magnetite, Shale, and granite-I using laser-induced breakdown spectroscopy. The graphical assessment and visualization endorse that the rock dataset series are positively skewed. Therefore, Frechet, Weibull, log-logistic, log-normal, and generalized extreme value distributions are considered as candidate distributions, and the parameters of these distributions are estimated by maximum likelihood and Bayesian estimation methods. The goodness of fit test and model selection criteria such as the Kolmogorov-Smirnov test, Akaike Information Criterion, and Bayesian Information Criterion are used to quantify the accuracy of the predicted data using theoretical probability distributions. The results show that the Frechet, Weibull, and log-logistic distributions are the best-fitted probability distribution for rock dataset. Cluster analysis is also used to classify the selected rocks that share common characteristics, and it is observed that diorite and gypsum are placed in one cluster.  However, slate, dolomite, marble, basalt, sandstone, schist, granite-II, and gneiss rocks belong to different clusters. Similarly, limestone and apatite appeare in one cluster. Likewise, shale, granite-I, magnetite, amphibolite, and hematitle appeare in a different cluster. The current work demonstrate that coupling of laser-induced breakdown spectroscopy with suitable statistical tools can identify and classify the rocks very efficiently.