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Objective. Investigation of the problems of zonal disintegration of rocks around deep underground workings in extremely small sampling, arising in geomechanical phenomena and processes in rock mass during mining. Methods . The primary tool used is numerical resampling methods, namely randomization, bootstrap, and Monte Carlo methods, which allow increasing the sample size, according to the available field data, to the required size for conducting a statistically sound analysis. Results. The problem of zonal fracture of rocks around deep underground workings is solved, for which the analytical dependence of the periodicity parameter of the defect function on the rock strength limit is estimated. The primary indicator of the statistical significance of the constructed model in work is the determination factor, based on which the type of analytical dependence under study is selected. Its deviation in the final model does not exceed 0.5% for any bootstrap sample volume, while in the other models considered in this paper, this value is achieved at n>200. Conclusion . The obtained interval estimates using bootstrap methods have a significant advantage over traditional approaches, increasing the reliability of the result in extremely small data samples without losing the level of significance.

Aim: to systematize data on the frequency and risk of bone fractures in patients with chronic pancreatitis. Methods. MEDLINE/PubMed, EMBASE, Cochrane, Google Scholar through October 2020 were searched to identify studies evaluating the prevalence of bone fractures in chronic pancreatitis. For the final analysis, publications with detailed descriptive statistics (total sample size, number of patients with chronic pancreatitis, number of control persons, number of patients with fractures in groups) were selected, allowing the resulting data to be included in the meta-analysis. Results. The final analysis included 6 studies involving 2 025 918 people (18 844 patients with chronic pancreatitis; 2 007 074 – control subjects). The generalized incidence of fractures in patients with chronic pancreatitis was 14.09% (95% CI: 5.877–25.098). There was significant heterogeneity between the results (p

Purpose of the study. The goal is to conduct a comparative analysis of the correlation of learning success with self-assessment of physical and mental status and objective health status, taking into account the influence of demographic and socio-economic variables in senior students of medical and humanitarian specialties Materials and methods. The study was conducted from 01.12. 2017 to 01.03.2019 at the Far Eastern Federal University and the Pacific State Medical University. The sample size was 410 students (207 (50.6%) female, 203 (49.4%) male, average age 21.5 (1.2) years), who at the time of the study were studying in 4–6 courses. Information on demographic parameters, social conditions of study, residence, subjective data on morbidity and appeal was collected using: a comprehensive questionnaire on student status of a university (Pozdeeva, 2008; with additions of authors). The objective state of health and the comorbidity index were investigated when studying the medical documentation of medical institutions attached: Form 025 / y; 001–1 / y; 062 / y. In the study of quality of life associated with health, we used the international questionnaire “A short form of self-assessment of quality of life related to health MOS SF-36”. Results. The total score of self-esteem of physical well-being among students of humanities was 66.1 points, among students of medical specialties 56.4 points. Academic performance was higher among students of both directions, marking their learning conditions as satisfactory and good (r = 0.034; r = 0.048 / r = 0.045; r = 0.065). Student performance was also higher for students in both areas, evaluating the quality of education as high (r = 0.032; r = 0.046 / r = 0.033; r = 0.043), but lower for students with a high comorbidity index (r = –0.038 / r = –0.036). We also found that an increase in the number of HRQoL points is accompanied by a significant increase in academic performance in students of both directions (r = 0.035; r = 0.045 / r = 0.033; r = 0.050). An analysis of the linear regression model describing the association of academic performance with variables in the pooled sample revealed that this indicator strongly correlates with the comorbidity index (r = 8.27), HRQoL (r = 7.28), quality of education, and family income (5.55 / 5.06). At the same time, academic performance had an unreliable relationship with age, individual income, and weakly correlated with the conditions of study and residence. Conclusion. Chronic morbidity among senior medical and humanitarian students is high (comorbidity index 1.5–1.7), but the total self-assessment of the quality of life associated with health is 59–62 points and falls within the normal range of values. Thus, despite the high level of chronic somatic pathology, students generally positively assess their physical and psychological status.

The most common inaccuracies and errors in the application of statistical methods found in Russian publications on soil science are considered. When designating random variables and distribution parameters in Greek letters, it is necessary to designate those that refer to general populations, and Latin letters – to sampling ones. A detailed description of the experiment and what the replications relate to allows you to draw correct conclusions from the study. It is necessary to avoid pseudoreplication when results at closely located sampling points are considered as characteristics of soil variability over large distances. Expanding the list of descriptive statistics will allow you to use a specific study in meta-analysis. Calculating the confidence interval for the average using the Student's test at different significance levels expands the scope of possible values of the average, but this approach is justified only if the indicator does not differ too much from the normal distribution. When testing statistical hypotheses, it is necessary to pay attention not only to the level of significance, but also to the power of the criterion. The normality distribution hypothesis can be tested using various criteria. The success of applying the criterion depends not only on the validity of the null hypothesis (a truly normal distribution), but also on other reasons: on the sample size and on the alternatives for which the criterion tests the hypothesis. Any statement about the type of relationship between features based on the correlation coefficient (Pearson or Spearman) is meaningless without specifying the number of replicates, since it is the number of replicates that determines the significance of the difference between the correlation coefficient and zero. It is proposed that authors and reviewers pay closer attention to such errors.

The aim of the study is the development of theoretical and methodological principles of the analysis of industry financial indicators. The relevance of the topic is confirmed on the one hand by the demand for industry indicators for all persons interested in financial and comparative analysis of enterprises, on the other hand by the complexity and lack of methods for deriving industry indicators of the financial analysis of enterprises.Materials and methods. The study used a system and comparative analysis, methods of economic and financial analysis of the financial statements of enterprises in the industry, and methods of statistical evaluation of the main parameters of the sample with a lognormal distribution. The main attention is paid to the use of multivariate statistical analysis, the use of the model of lognormal distributions recommended for distributions with pronounced right-hand asymmetry. As the statistical material, the accounting data of the enterprises of the industry for the extraction of crude oil and natural gas for 2016 were used. The sample size was 185 enterprises. In the course of the study, the authors solved the following tasks: proposed stages of analysis for determining industry financial indicators, tested the hypothesis of a lognormal distribution of marginal distributions of the main financial indicators of the sample, tested the hypothesis of a jointly normal distribution of a multi-factor random vector of financial indicators of the sample, obtained the most likely values of financial analysis indicators for the industry of crude oil and natural gas production.Results. The theoretical significance of the work is the algorithm proposed by the authors for calculating industry-specific indicators of financial analysis, characterized by obtaining modal values based on the analysis of the multidimensional logarithmically normal distribution of the vector of financial indicators of a sample of enterprises. In the course of the study, the authors obtained distributions for the main indicators with a pronounced right-hand asymmetry and tested the hypothesis of the lognormal distribution of marginal distributions. The paper presents an algorithm for testing the hypothesis of joint normality of a ninedimensional random vector. Median and modal values of industry and financial indicators were obtained. The authors analyzed the differences between the median and modal results of the study. For analysis, a three-dimensional random vector is considered, including revenue, return on equity and turnover of accounts receivable. The difference between median and modal results is explained by the right-hand asymmetry of the distribution. The recommendations, given by the authors for determining industry indicators of financial analysis of enterprises in the industry for the extraction of crude oil and natural gas are practical in nature and are applicable to all industries.Conclusion. In the work, it is shown that the orientation toward generally established recommended values of coverage indicators, financial leverage, immobilization, profitability and turnover seems incorrect due to the variety of specific features of enterprises in various industries. We recommend calculating the most likely industry coefficients by groups depending on the size of the enterprise (revenue or capitalization).

Aim. To test a hypothesis of hypoperfusion-induced white matter changes in patients with atrial fibrillation (AFib) and to present statistics to compute sample size for the upcoming studies.Material and methods. We included 30 inpatients with AFib and investigated them with magnetic resonance imaging (MRI) with standard sequencies and diffusion tensor imaging (DTI). DTI data were analyzed with conventional ROI analysis in the Olea Sphere software and with watershed areas (WSA) mask in the FSL toolbox after nonlinear transformation of images to the Montreal Neurological Institute (MNI) space. Wilcoxon test was used to compare diffusion characteristics across subgroups.Results. Median age of participants was 73 years (69-78), 18 (60%) patients had moderate signs of small vessel disease with Fazekas score of one. Twenty-one patients had paroxysmal AFib. Analysis of WSA revealed decreased white matter integrity in the parieto-occipital cortical WSA with a pattern of significantly increased mean diffusivity (p=0,039), and marginally significant decrease in fractional anisotropy (p=0,056). Rank-based effect size across areas under comparison was either small (0,2) or negligible, and with statistical power in the range of 0,05-1.Conclusion. Atrial fibrillation could have pathophysiologically feasible mechanism to affect white matter integrity in the watershed areas.

The article quantified the relative importance of social, general and specific professional requirements for the individual head of the internal affairs; requirements are considered as an empirical analogue of the institutional conditions for its performance, reliability estimates as the degree of unity experts. Methods of determining the evaluation of the significance and reliability of these estimates are based on the use of statistical analysis techniques. Thus, the assessment of the value is defined as the arithmetic mean of the ordinary, the reliability of which, however, as the main result of the survey of experts is far from obvious: big themselves magnitude of significance, however, may prove to be very unreliable values. In view of the foregoing, in this case it can be lost very feasibility of obtaining the individual assessment of the head as well as his activities as unreliable foundation as low reliability significances means a loss of confidence in the guarantees of the individual manager. The mathematical tool for evaluating the reliability indicator here is the spread of expert data - the dispersion of experts’ opinions expressed in quantitative terms, which allows comparison of significances, placing them on the priorities. To improve the reliability assessment of the arithmetic mean pre-treatment censoring sample expert values ​​has been made - prior their ordering ascending (construction of an ordered series), followed by cutting off in equal amounts (10% of the sample size), the extreme members of the series, on what basis and carried out the final calculation the arithmetic mean. Increased reliability is achieved at the same time due to exclusion from the collection of expert data of those who could potentially be the result of being obsessed with excessive caution or individual experts.

Статья посвящена двухточечным моментам решений, возникающих в простых лагранжевых моделях для уравнения индукции в случае конечного корреляционного времени случайной среды. Рассматривается вопрос о связи коммутационных свойств соответствующих алгебраических операторов с минимальным объемом выборки независимых случайных реализаций, который необходим в численном эксперименте для моделирования двуточечного коррелятора решения. Показано, что, как и для одноточечных моментов, численное исследование двуточечного коррелятора в случае коммутирующих операторов (случайные числа) требует существенно меньших объемов выборки, чем в случае, когда они не коммутируют (случайные матрицы)., This paper is devoted to the two-point moments of the solutions arising in simple Lagrange models for the induction equations in the case of finite correlation time of a random medium. We consider the question on the connection between the commutative properties of the corresponding algebraic operators and the minimal sample size of independent random realizations necessary in numerical experiments for modeling the two-point correlator of the solution. It is shown that, as for the one-point moments, the numerical study of the two-point correlator in the case of commutating operators (random numbers) requires a much smaller sample size than in the case when they do not commute (random matrices)., ВЫЧИСЛИТЕЛЬНЫЕ МЕТОДЫ И ПРОГРАММИРОВАНИЕ: НОВЫЕ ВЫЧИСЛИТЕЛЬНЫЕ ТЕХНОЛОГИИ, Выпуск 3 2017

This study examined factors influencing the probability of farmers accessing agricultural credit as well as the amount of received credit allocated to farming operations in the Bole district of Northern region, Ghana. A sample size of 100 respondents were randomly selected and interviewed through a well-structured questionnaire. Paired sample t-test was used to test whether there exist a significant difference between the amount of credit received and the amount allocated to farm sectors. Probit model was employed to identify factors influencing the probability of farmer’s access to agricultural credit while Tobit regression model was used to estimate the determinants of credit allocated to farm operations. Evidence from the paired-sample t-test indicated a significance difference between amount of credit received and amount allocated to farm operations. The results from the Probit model indicated that gender, household size, farmers engaging in off-farm income and membership of farmer-based-organization exert significant influence on the probability of farmer’s access to agricultural credit. Moreover, estimates from the Tobit regression model revealed that the amount of credit farmers allocate to farm sector is significantly influence by sex of the farmer, farmers level of education, the size of loan received, loan delay (number of days between loan application and receipt) as well as farmers receiving extension services. The study therefore recommends that loan applications should be approved on time to enable farmers used it for the intended purposes, and farmers should be advised through effective extension programs on the need to use loans for the purpose for which it was procured.

Reliability is the main indicator of the quality of special purpose equipment/systems, which are in their service life exposed to extreme operating modes and environmental conditions. Reliability of electronic equipment/systems is difficult to determine analytically, specially for repairabile systems with a large number of elements because of a large number of possible system states, which requires setting up and solving a system of a large number of equations. Therefore, simulation methods are applied to determine the reliability of electronic equipment/systems. This paper examines the accuracy of the point estimate of reliability calculated by the Monte Carlo simulation method depending on the sample size n, and the number of iterations (repetitions of calculation), Np.