Document Type : Original Research Paper


1 Department of Statistics, King Abdullah Campus Chatter Kalas, The University of Azad Jammu & Kashmir, Muzaffarabad, Pakistan

2 Department of Physics, King Abdullah Campus Chatter Kalas, The University of Azad Jammu & Kashmir, Muzaffarabad, Pakistan


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.


[1]. Noori, M. Khanlari, G. Rafiei, B. Sarfarazi, and V. Zaheri, M. (2022). Correction to: Estimation of Brittleness Indices from Petrographic Characteristics of Different Sandstone Types (Cenozoic and Mesozoic Sandstones). Markazi Province, Iran, 55, 6519.
[2]. Yavari, M. D. Haeri H. Sarfarazi, V. Fatehi M. and Lazemi, H. A. (2021). Compressive Failure Analyses of Rock-like Materials by Experimental and Numerical Methods, Journal of Mining and Environment. 12 (3): 769-783.
[3]. Sarfarazi, V. Haeri, H. and Fatehi M. (2021). On Direct Tensile Strength Measuring of Anisotropic Rocks. Journal of Mining and Environment. 12 (2): 491-499
[4]. Zaman, M. A. Rahman, A. Haddad, K. and Hagare, D. (2012). Identification of the best fit probability distributions in at-site flood frequency analysis: A case study for Australia using 127 stations. Hydrology and Water Resources Symposium, 939-945.
[5]. Azizi, M.A. Karamadibrata, S. Wattimena, R.K. and Sidi, I.D. (2013). Characterization of the distribution of physical and mechanical properties of rocks at Tatupan coals mine, South Kalimanta, Indonesia. Rocks Mechanics and Resources Energy and Engineering, 79, 213-216.
[6]. Ghazdali, O. Guemouria, A. Rziki, S. and Moustadraf, J. (2021). Statistical analysis of rocks mass using data mining technique: a study case in Morocco. Journal of Physics: Conference Series. 1743 (1): 107-114.
[7]. Malkowski, P. Niedbalski, Z. and Balarabe, T. (2020). A statistical analysis of geomechanical data and its effect on rock mass numerical modeling: a case study. International Journal of Coal and Science Technology. 8 (2): 312-323.
[8]. Teymen, A. and Menguc, E.C. (2020). Comparative evaluation of different statistical tools for the prediction of uniaxial compressive strength of rocks. International Journal of Mining Science and Technology. 30 (6): 785-797.
[9]. Gent, V. Almeida, E. and Hofland, B. (2019). Statistical analysis of the stability of rock slopes. Journal of Marine Sciences and Engineering. 7 (3): 60- 75.
[10]. Cai, X. Zhou, Z. Liu, K. Du, X. and Zang, H. (2019). Water weaking effects on the mechanical behavior of different rock types: phenomenon and mechanics.  Applied Sciences. 9 (20): 4450.
[11]. Salih, H. S. and Alshkane, Y. (2018). Statistical analysis of physical and mechanical properties of igneous rocks. Journal of Garmian University. 5 (2): 174-189.
[12]. Mayer, J.M. Allen, D.M. Gibson, H.D. and Mackie, D.C. (2014). Application of statistical approaches to analyze geological, geotechnical, and hydrogeological data at a fractured- mine site in northern Canada. Hydrogeology Journal. 22 (7): 1707-1723.
[13]. Karakul, H. and Ulusay, R. (2013). Emprical correlations for predicting strength properties of rocks from P-wave velocity under different degree of saturation. Rock Mechanics and Rock Engineering. 46 (5): 981-999.
[14]. Ceryan, N. Okkan, U. and Kesimal, A. (2012). Application of the generalized regression neural networks in predicting the Unconfined Compressive Strength of carbonate rocks. Rock Mechanics and Rocks Engineering. 45 (6): 1055-1072.
[15]. Ghazvinian, A. and Hadei, M. R. (2012). Effect of discontinuity orientation and confinement on the strength of jointed anisotropic rocks. International Journal of Rock Mechanics and Mining Sciences. 55 (1): 117-124.
[16]. Huang, S. Xia, K. Yan, F. and Feng, X. (2010). An experimental study of the rate dependence of tensile strength softening of Longyou sandstone. Rock Mechanics and Rock Engineering. 43 (6): 677-683.
[17]. Huang, W. Xing, W. Chen, S. Yang, L. and Wu, K. (2017). Experimental study on sedimentary rock’s dynamic characteristics under creep state using a new type of testing equipment. Advanced in Materials Sciences and Engineering, 1, 1155-1168
[18]. Liu, Z. Guo, Y. Du, S. Wu, G. and Pan, M. (2017). Research on calibrating rock mechanical parameters with a statistical method. Economic Geology. 58 (8): 1246-1266.
[19]. Mibei, G. (2014). Introduction to types and classification of rocks. Geothermal Development Company, 51(6), 143-155.
[20]. Rybar, P. Strba, L. Molokac, S. and Hvizdak, L. (2015). Study of physical-mechanical rock properties for rock disintegration purposes. Podzemni radovi. 21 (5): 131-133.
[21]. Singh, T. N. Kainthola, A. and Venkatesh, A. (2012). Correlation between point load index and uniaxial compressive strength for different rock types. Rock Mechanics and Rock Engineering. 45 (2): 259-264.
[22]. Wang, M. Wan, W. and Zaho, Y. (2019). Prediction of uniaxial compressive strength of rocks from simple index tests using a random forest predictive model. Rock Mechanics and Rock Engineering. 348 (1): 3-32.
[23]. Zadhesh, J. and Majdi, A. (2022). Determining Probability Distribution Functions of Rock Joint Geometric Properties,  Journal of Mining and Environment (JME) Vol. 13, No. 1, 2022, 281-308.
[24]. Ahmed, N. Awan, J.A. Fatima, K. Iqbal, S.M.Z. Rafique, M. Abbasi, S. A. and Baig, M. A. (2022). Machine learning-based calibration LIBS analysis of aluminium-based alloys. Eur. Phys. J. Plus., 137, 671.
[25]. Ahmed, N. Ahmed, R. and Baig, M.A. (2017). Analytical Analysis of Different Karats of Gold Using Laser Induced Breakdown Spectroscopy (LIBS) and Laser Ablation Time of Flight Mass spectrometer (LA-TOF-MS). Plasma Chem Plasma Process, 38, 207-222.
[26]. Umar, Z.A. Ahmed, N. Ahmed, R. Liqat, U. and Baig, M.A. (2018). Elemental composition analysis of granite rocks using LIBS and LA-TOF-MS. Applied Optics, 57, 4985-4991.
[27]. Ahmed, N. Zeshan, A. Umar, Z.A. Ahmed, R. and Baig, M.A. (2017). On the elemental analysis of different cigarette brands using laser induced breakdown spectroscopy and laser-ablation time of flight mass spectrometry. Spectrochimica Acta Part B 136, 39–44.
[28]. Ahmed, N. Ahmed, R. Umar, Z. A. Liaqat, U. Manzoor U. and Baig, M. A. (2018). Qualitative and Quantitative Analyses of Copper Ores collected from Baluchistan. Pakistan using LIBS and LA-TOF-MS, Applied Physics B, 124, 160.
[29]. Akhtar, M. Jabbar, A. Mehmood, S. Ahmed, N. Umar, Z.A. Ahmed, R. and Baig, M.A. (2018). Magnetic Field Enhanced Detection of Heavy Metals in Soil using Laser Induced Breakdown Spectroscopy. Spectrochimica Acta Part B 148 143–151.
[30]. Abbas, K. and Tang, Y. (2015). Analysis of Frechet distribution using reference priors. Communications in Statistics-Theory and Methods. 44 (14): 2945–2956.
[31]. Sun, D. (1997). A note on non-informative priors for Weibull distributions. Journal of Statitical Planning and Inference.
[32]. Abbas, K. and Tang, Y. (2016). Objective Bayesian Analysis for Log-logistic Distribution. Communications in Statistics-Simulation and Computation, 45, 2782–2791.
[33]. Kolmogorov, A.N. (1933). Sulla determinazione empirica di una legge di distribuzione.  Giornale dell, Instituto Italiano degli Attuari, 4, 83-91.
[34]. Kruskal, W.H. and Wallis, W.A. (1952). Use of ranks in one-criterion variance analysis. Journal of the American Statistical Association. 47 (260): 583-621.