The application of multidimensional distribution functions of grained materials’ properties for evaluation of beneficiation processes

The paper presents a way of determining relations between ash content in coal, particle size and particle density by means of regression, multidimensional Morgenstern distribution functions and kernel approximation. The three-dimensional random vector (D, ?, ?), where D is a random variable describing particle size, ? - random variable describing particle density and ? - random variable describing ash content, where function ?=?(d, ?) is obtained by means of regressive function. The multidimensional Morgenstern distribution functions and kernel estimators with the use of Gauss function were applied to approximate the functions f(d, ?, ?) and f1(d, ?). This approach is a new way of multidimensional description of grained materials such as coal and it also allows to evaluate material features more properly than the classical statistical approach. The results were verified statistically.