Abstract
Statistical and geometric patterns were disclosed that are inherent to extremely asymmetric types of formation of stochastic frequencies of geofeatures values with the help of the exponential, probabilistic, structural, and Zipf distribution laws, which are most often used to describe them. A sophisticated pattern with exponential and hyperbolic nature of the probabilistic frequencies formation development was found. Based on these features, a leading concept of using major structure-forming characteristics of the distribu- tion of variable parameters as desired theoretical distribution function was used for parameterization of an extremely asymmetric distribution model. A median and modal frequency of geofeatures distribution were defined as the theoretical parameters of the desired distribution model. A structure was constructed and formulas were derived for determination of the statistical characteristics of the recommended distribution model. Approbation of the distribution model was conducted on an example of morphometric signs empirical distributions among the localities of varying complexity and qualitative indicators of a number of gold and rare metal deposits; inhesion of its approxi- mating power and flexibility of use was revealed.
Highlights
Substantiation of a rational distribution model was carried out by generalizing the properties of extremely asymmetric types of geofeatures’ distribution among the objects of georesources of varying complexity.According to the analysis of extremely asymmetric types of empirical distributions assessment practices it was found that the distribution of maximum relief and heights of evenly spaced points in the upland and foothill areas, as well as the distribution of quality indicators of gold and rare metal deposits often correspond to these types of distributions; that the theoretical distributions favorably describing these types of distributions are scarce due to the diversity of their frequencies formation
A leading concept used with regard to the extremely asymmetric distribution types was that of providing their structural empirical parameters as theoretical parameters of the desired distribution function
Distributions used to describe the extremely asymmetric distributions of quality indicators of the gold and rare metal mineral deposits, and morphometric features of complex relief areas are scarce, due to the variety of their forms, the exponential and other distributions often used to describe them do not cover a wide range of highly-varying types of asymmetric distributions of the geofeatures
Summary
Substantiation of a rational distribution model was carried out by generalizing the properties of extremely asymmetric types of geofeatures’ distribution among the objects of georesources of varying complexity. The statistical geometric regularities inherent to extremely asymmetric distributions of geofeatures were studied. For this purpose, the most common indicative, structural and probabilistic and Zipf ’s distribution laws were used. It was found that the extreme types of asymmetric distribution are characterized by rather complex pattern including exponential and hyperbolic nature of probability frequencies formation development. Based on these features, a leading concept used with regard to the extremely asymmetric distribution types was that of providing their structural empirical parameters as theoretical parameters of the desired distribution function. Use of sustainable median unbiasedness property and its consistency in the assessment allowed to increase the approximation power and flexibility of the recommended distribution, which were strengthened by parametric conversion of the feature in the median lobes, thereby allowing us to obtain more reliable results and reduce the risk in the case of small values and uncertainties of statistical sampling that is important in the assessment of the extremely asymmetric types of empirical distributions
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