Abstract

Mathai's pathway model is playing an increasingly prominent role in statistical distributions. As a generalization of a great variety of distributions, the pathway model allows the studying of several non-linear dynamics of complex systems. Here, we construct a model, called the Pareto-Mathai distribution, using the fact that the earthquakes' magnitudes of full catalogues are well-modeled by a Mathai distribution. The Pareto-Mathai distribution is used to study artificially induced microseisms in the mining industry. The fitting of a distribution for entire range of magnitudes allow us to calculate the completeness magnitude (M-c). Mathematical properties of the new distribution are studied. In addition, applying this model to data recorded at a Chilean mine, the magnitude M-c is estimated for several mine sectors and also the entire mine.