Distribution Parameters Research Articles

Revisiting the Use of the Gumbel Distribution: A Comprehensive Statistical Analysis Regarding Modeling Extremes and Rare Events

The manuscript presents the applicability of the Gumbel distribution in the frequency analysis of extreme events in hydrology. The advantages and disadvantages of using the distribution are highlighted, as well as recommendations regarding its proper use. A literature review was also carried out regarding the methods for estimating the parameters of the Gumbel distribution in hydrology. Thus, for the verification of the methods, case studies are presented regarding the determination of the maximum annual flows and precipitations using nine methods for estimating the distribution parameters. The influence of the variability of the observed data lengths on the estimation of the statistical indicators, the estimation of the parameters, and the quantiles corresponding to the field of small exceedance probabilities (p < 1%) is also highlighted. In each case, the results are analyzed compared to those obtained with the Generalized Extreme Value distribution, the four-parameter Burr distribution, and the five-parameter Wakeby distribution estimated using the L-moments method. The results of the case studies highlight and reaffirm the statistical, mathematical, and hydrological recommendations regarding the avoidance of applying the Gumbel distribution in flood frequency analysis and its use with reservations in the case of maximum precipitation analysis, especially when the statistical indicators of the analyzed data are not close to the characteristic ones and unique to the distribution.

Bootstrap Methods for Bias-Correcting Probability Distribution Parameters Characterizing Extreme Snow Accumulations

Accurately quantifying the threat of collapse due to the weight of settled snow on the roof of a structure is crucial for ensuring structural safety. This quantification relies upon direct measurements of the snow water equivalent (SWE) of settled snow, though most weather stations in the United States only measure snow depth. The absence of direct load measurements necessitates the use of modeled estimates of SWE, which often results in the underestimation of the scale/variance parameter of the distribution of annual maximum SWE. This paper introduces a novel bias correction method that employs a bootstrap technique with regression-based models to calibrate the variance parameter of the distribution. The efficacy of this approach is demonstrated on real and simulated datasets. The findings reveal varied levels of success, with the efficacy of the proposed approach being inherently dependent on the quality of the selected regression-based model. These findings demonstrate that integrating our approach with a suitable regression-based model can produce unbiased or nearly unbiased annual maximum SWE distribution parameters in the absence of direct SWE measurements.

Evaluation of wood chips terminal velocity and some morphological properties in a wind tunnel experiment

AbstractThe removal of wood dust and chips from the work area is also important for occupational health safety regulation and to avoid the risk of fire and dust explosion. Knowledge of the terminal velocity is an important condition for the effective and economical operation of commonly used wood dust-chip extraction systems. While the largest particles are important from the point of view of the operation of the extraction system, knowledge of the terminal velocity of small particles (under 1 mm) is desirable from the point of view of separation and occupational health safety. New measuring and calculation method is developed in order to determine the terminal velocity of wood particles. We built an experimental device to measure the terminal velocity of wood dust-chip particles, and using the experimental results, we modified the calculated terminal velocity based on the modified equivalent particle density (100–130 kg/m3) in the 1–150 μm size range. The terminal velocity of wood particles under 150 μm more and more deviates from the theoretical values. As a result of mechanical processing, the resulting wood particles’ shape is in most cases flat. The average thickness of the wood particles is mainly determined by the sawing parameters. The flat shape of particles increases the specific surface area in a certain extent depending on the distribution parameters.

Chen-Burr XII Model as a Competing Risks Model with Applications to Real-Life Data Sets

In this paper Chen-Burr XII distribution is constructed and graphical description of the probability density function, hazard rate and reversed hazard rate functions of the proposed model is obtained. Also, some statistical characteristics of the Chen-Burr XII distribution are discussed and some new models as sub-models from the Chen-Burr XII distribution are introduced. Moreover, maximum likelihood estimation of the parameters, reliability, hazard rate and reversed hazard rate functions of the Chen-Burr XII distribution are considered. Also, the asymptotic confidence intervals of the distribution parameters, reliability, hazard rate and reversed hazard rate functions are presented. Finally, three real life data sets are applied to prove how the Chen-Burr XII distribution can be applied in real life and to confirm its superiority over some existing distributions.

Short-Circuit Current Calculation of Flexible Direct Current Transmission Lines Considering Line Distribution Parameters

Short-Circuit Current Calculation of Flexible Direct Current Transmission Lines Considering Line Distribution Parameters

Two sunspot group populations and Gnevyshev-Waldmeier rule

Based on the materials of the Royal Greenwich Observatory catalog, the study of two different sunspot group populations continued: LLG – large long-lived, and SSG – small short-lived groups. The task of achieving a higher accuracy of the population separation parameter than before (Nagovitsyn & Pevtsov 2016, 2021) is being solved. A procedure for randomizing the lifetimes of sunspot groups observed once a day is proposed, which allows for statistical studies to achieve a higher time resolution. The form of the Gnevyshev-Waldmeier Rule is taken, which linearly connects the logarithm of the logS area and the lifetime of the sunspot group LT (over limited time intervals). It is shown that it has coefficients significantly different for SSG and LLG populations. The range of values of the group lifetime parameter separating the populations was found as LT∗=4.75±0.53 days, which is in agreement with the threshold values obtained earlier for the number of days of sunspot group observation: mSSG⩽5 days and mLLG>5 days. It is shown that the parameters of the bilognormal distribution of the sunspot group areas, obtained from their common grouped sample statistically by Levenberg–Marquardt method and with a preliminary division into lognormal distributions by lifetime, correspond to each other. It was clarified that, with an accuracy of up to a tenth of a day, the SSG population corresponds to the lifetimes of groups ⩽4.6 days, and the LLG population corresponds to times ⩾4.7 days. The results obtained make it possible to study various physical properties of SSG and LLG populations independently of each other in order to compare them and study their nature.

Optimal Internality Taxation of Product Attributes

This paper explores how a benevolent policymaker should optimally tax (or subsidize) product attributes when consumers are behaviorally biased. We demonstrate that market choices are informative about biases, which can be exploited for targeting biased consumers via a nonlinear tax schedule. We show that the properties of this schedule depend on few parameters of the joint distribution of consumer valuations and biases. Furthermore, we provide a novel justification for behaviorally motivated product standards and derive when a combination of taxes and standards is optimal. We illustrate our findings based on a numerical example from the lightbulb market. (JEL D82, D91, H21, H25, L69)

Hierarchical Virtual Screening of SARS-CoV-2 Main Protease Potential Inhibitors: Similarity Search, Pharmacophore Modeling, and Molecular Docking Study

Background: The outbreak of COVID-19 caused by severe acute respiratory syndrome coronavirus2 (SARS-CoV-2) resulted in a widespread pandemic. Various approaches involved the repositioning of antiviral remedies and other medications. Several therapies, including oral antiviral treatments, represent some approaches to adapting to the long existence of the COVID-19 pandemic. In silico studies provide valuable insights throughout drug discovery and development in compliance with global efforts to overcome the pandemic. The main protease is an essential target in the viral cycle. Computer-aided drug design accelerates the identification of potential treatments, including oral therapy. Aims: This work aims to identify potential SARS-CoV-2 main protease inhibitors using different aspects of in silico approaches. Methods: In this work, we conducted a hierarchical virtual screening of SARS-CoV-2 main protease inhibitors. A similarity search was conducted to screen molecules similar to the inhibitor PF-07321332. Concurrently, structure-based pharmacophores, besides ligand-based pharmacophores, were derived. A drug-likeness filter filtered the compounds retrieved from similarity search and pharmacophore modeling before being subjected to molecular docking. The candidate molecules that showed higher affinity to the main protease than the reference inhibitor were further filtered by absorption, distribution, metabolism, and excretion (ADME) parameters. Results: According to binding affinity and ADME analysis, four molecules (CHEMBL218022, PubChem163362029, PubChem166149100, and PubChem 162396459) were prioritized as promising hits. The compounds above were not reported before; no previous experimental studies and bioactive assays are available. Conclusion: Our time-saving approach represents a strategy for discovering novel SARS-CoV- 2 main protease inhibitors. The ultimate hits may be nominated as leads in discovering novel SARS-CoV-2 main protease inhibitors.

Comparative study of two-phase flow approaches for modeling conjugate heat transfer in a three-dimensional wavy microchannel-heat sink with CuO-water nanofluid

This study aims to numerically investigate the conjugate heat transfer (CHT) and the changes in the hydraulic and thermal terms of laminar flow (300 ≤ Re ≤ 800) in a 3-D wavy microchannel heat sink (MCHS). The obtained results from different nanofluid flow simulated models will be compared. The numerical simulation approaches used include single-phase, mixture, Eulerian, DPM, and DDPM. The effect of adding 1%, 3%, and 6% concentration of CuO nanoparticles (100 nm) in deionized water as the base fluid is examined on various parameters such as local and axial temperature, heat transfer convective coefficient, friction factor, Nusselt number (Nu), velocity distribution, and thermal and hydraulic boundary layer parameters. The substrate surface, due to its larger area surface and the amplitude of the sinusoidal wave, has a greater impact on the nanofluid flow as a channel bottom conjugate surface compared to others. The results obtained from the different models show close agreement with each other for various cases. For example, at Re = 304, the average Nu and friction factor for pure water are approximately 10.43 and 0.0260, respectively. For water with 0.01 concentration of CuO nanoparticles, Nu is found to be in the range of 10.43–10.78, and the friction factor ranges from 0.260 to 0.290, depending on the approach used for simulation. This shows a 2% increase in Nusselt number compared to a 0.05% increase in the friction factor. Moreover, these values increase by approximately 5.7% and 11.3% on average with an increase in CuO nanoparticle concentration to 0.06. Additionally, the DPM and DDPM models show a 15% difference in the scattering of CuO nanoparticles compared to the Eulerian-Eulerian models. The single-phase model presented in this study yields similar results to the multiphase approaches. Furthermore, the PEC parameter increases by about 1.9% with the addition of CuO nanoparticles at a concentration of 0.06.

Dynamics of axially moving spinning microbeams composed of tri-directional graded porous materials with axisymmetric cross-sections and piezoelectric layers in complex fields

The current article appraises the vibration and stability of tri-directional functionally graded porous microscale beams with rectangular cross-sections integrated with piezoelectric layers under spinning and axial movements in complex environments. The microbeam is surrounded by a three-parameter Winkler-Pasternak-Hetenyi medium, and its material characteristics are graded in thickness, width, and longitudinal spatial directions by considering non-uniform and uniform porosity models. Dynamic equations, vibration frequencies, and stability criteria of the system are determined with the aid of the Galerkin approach and Laplace transform. The Campbell diagram and stability maps are drawn. Frequency and stability analyses, as well as comparison and parametric analyses, are conducted. The impacts of piezoelectric voltage, magneto-hygro-thermal fields, axial and tangential distributed follower forces, substrate characteristics, scale parameter, aspect ratio, porosity factor, and material gradation on flutter and divergence instability boundaries are assessed in detail. It is deduced that instability regions are condensed, and the instability threshold is enhanced by fine-adjusting the porosity and material gradient. It is discovered that destructive environmental effects can be alleviated by regulating the piezoelectric voltage. In addition, compared with the case of a square cross-section, the divergence/flutter instability region of the microbeam with a rectangular cross-section is smaller/larger. The outcomes of the present research can be helpful in the design of next-generation bi-gyroscopic systems.

Fitting COVID-19 datasets to a new statistical model

This paper discussed gull alpha power Weibull distribution with a three-parameter. Different statistical inference methods of Gull Alpha Power Weibull distribution parameters have been obtained, estimated, and evaluated. Then, the results are compared to find a suitable model. The unknown parameters of the published Gull Alpha Power Weibull distribution are analyzed. Seven estimation methods are maximum likelihood, Anderson–Darling, right-tail Anderson–Darling, Cramér–von Mises, ordinary least-squares, weighted least-squares, and maximum product of spacing. In addition, the performance of this distribution is computed using the Monte Carlo method, and the limited sample features of parameter estimates for the proposed distribution are analyzed. In light of the importance of heavy-tailed distributions, actuarial approaches are employed. Applying actuarial criteria such as value at risk and tail value at risk to the suggested distribution shows that the model under study has a larger tail than the Weibull distribution. Two real-world COVID-19 infection datasets are used to evaluate the distribution. We analyze the existence and uniqueness of the log-probability roots to establish that they represent the global maximum. We conclude by summarizing the outcomes reported in this study.

Effect of distribution parameters on the noise spectrum of bubble clusters

This study explores the effects of bubble distribution parameters on the noise spectrum of bubble clusters through direct numerical simulations across volume fractions from 0.005% to 40%. Three types of bubble cluster distributions were analyzed: layered (uniformly sized bubbles with layered positioning), random (uniformly sized bubbles with random positioning), and lognormal (log-normally distributed bubble sizes with random positioning). Using the Ffowcs Williams–Hawkings (FW–H) method, we evaluated the sound pressure levels of the clusters. We found that the arrangement of bubble positions has little impact on the collapse times of bubble clusters. At volume fractions greater than 0.5%, bubble size also shows minimal effect on collapse times. However, when the volume fraction is less than 0.5%, the collapse times gradually approach the collapse time of the largest bubble in the cluster in a free field. Noise spectrum analyses showed that the arrangement of bubble positions significantly influences the noise spectra within the volume fraction range of 0.5%–25%, but has minimal impact outside this range. Importantly, the distribution of bubble sizes shows negligible effects on the noise spectrum, demonstrated by the nearly identical sound pressure level octave decay rates for random and lognormal clusters at the same volume fractions. This consistency can be mathematically described by the fitting formula: decay rate (dB/octave) = 18.192 × α−0.047−16.264. These findings enhance our understanding of the noise spectrum across varied bubble cluster distributions and provide new insights into the mechanisms of cavitation noise.

Exploration and optimization of novel replacement and prefetching strategies for inefficiencies of advanced MRAM-based hybrid cache systems

With the emergence of cutting-edge hardware systems such as cloud computing, edge computing, and on-chip neural network accelerators, how to design advanced memory strategies to substitute the traditional ones for maximizing the potential performance of non-volatile memory (NVM) under the existing hardware conditions, has become an urgent research issue for both academia and industrial communities. It is promising and innovative to improve computer systems in the layer of data exchanging with the emerging advanced semiconductor devices. In the paper, to address the inefficiencies of write-intensive, high power consumption, low hit rate and so on, which exist in hybrid magnetic random access memory cache systems, three novel cache replacement strategies and two cache prefetching strategies are put forward. The proposed triple novel replacement strategies, including historical frequency and time judgments, duplicate data-aware deletion, and dynamic relevance factors computing, can be utilized to compensate for the shortcomings of the traditional least recently used replacement strategy, respectively. In the two novel prefetching strategies, region distribution parameters and Listnet ranking network are imported into the caching process, respectively, to achieve optimized hitting performance. The simulation results demonstrate that the proposed replacement strategies can achieve up to 61.76%, 84.91%, 56.49%, and 53.21% optimization of write count, hit rate, dynamic power, and IPC compared to the conventional one. The proposed prefetching strategy can achieve up to 91.27%, 49.25% hit rate and IPC optimization. Meanwhile, the synthetic evaluation of the replacement and prefetching strategies are elaborated in the paper, including multi-core characteristics, information entropy, interplays and the performance constraints between replacement and prefetching mechanism, which would facilitate more credible ideas for future memory inefficiencies management and strategy design.

Change point detection in length-biased lognormal distribution

In this paper, we develop two procedures for identifying the dynamic trends in the parameters of length-biased lognormal distribution based on likelihood ratio and modified information criterion. These methods mainly consider the test of the existence of the change point and provide the maximum likelihood estimation of the change point when the change point exists. In addition, the asymptotic distribution of test statistic based on likelihood ratio is derived as an extreme value distribution, while the asymptotic distribution of test statistic based on modified information criterion is derived as a chi-square distribution. And the consistency of parameter estimation is proved. Simulations are conducted to study the performance of the proposed method in terms of power, coverage probabilities and average sizes of confidence sets. The proposed methods are applied to a real data to illustrate the detecting procedures.

Statistical inference for marshall-olkin bivariate Kumaraswamy distribution under adaptive progressive hybrid censored dependent competing risks data

Abstract The statistical inference under competing risks model is of great significance in reliability analysis and it is more practical to assume that they have dependent competing causes of failure in actual situations. In this article, we make inference for unknown parameters of a Marshall-Olkin bivariate Kumaraswamy distribution under adaptive progressive hybrid censoring mechanism. The maximum likelihood estimations of the unknown parameters are derived, and the Fisher information matrix is then employed to construct asymptotic confidence intervals. Bayes estimates are evaluated against squared error and linex loss functions assuming ordered Gamma-Dirichlet and Gamma-Dirichlet prior distributions for order restriction and without order restriction cases respectively. The Metropolis-Hasting and Lindley techniques are applied to acquire the estimates of all unknown parameters. A thorough simulation analysis is demonstrated to assess the performance of the supplied approaches across various sample sizes. The usefulness of the techniques is illustrated using real engineering data to prove their versatility in practical applications.

A method for assessing the operational status of a microseismic monitoring system using energy distribution changes of observed data

Abstract The operational status of geophones plays a pivotal role in ensuring the accuracy and reliability of microseismic monitoring systems. However, conventional techniques used to evaluate the operational status of geophones require human intervention or significant time delays. To address this issue, we propose a method for online monitoring of geophone status using observed data obtained from a microseismic system. Firstly, the energy features of the preprocessed observation data are extracted via wavelet packet decomposition. Subsequently, the distribution parameters of energy features are obtained through loglogistic distribution fitting. These parameters are then applied to a change-point detection model, enabling the online monitoring of seismic geophones. In addition, we selected long short-term memory (LSTM) network to classify the operational status of the geophones, which is trained using the obtained energy distribution data and the time-frequency characteristics of the observed data. The experimental results indicate that the model achieves an accuracy of 98.33%, surpassing the 89.58% accuracy of the support vector machine (SVM). The proposed method not only contributes to online monitoring and precise determination of the operating status of detectors, but also has enormous application potential in other fields that require monitoring and evaluating the operating status of instruments.

Fisher information contained in incomplete observations

The accuracy of statistical estimates of unknown distribution parameters depends not only on the bulk of sampling data but also on the method of data acquisition. The information content of experimental data is one of the basic requirements. Problems of mathematical statistics, in particular parametric estimation based on censored observations, have specific features. Typical representatives of models of incomplete observations on a straight line are models of random censoring, competing risks of (single, multiple) random censoring. The purpose of this study is to show that censoring does not always lead to loss of (Fisher) information. It is shown that if censoring is informative, i.e., the distribution of censoring random variables depends on the same parameter, it is possible to specify a model where information can be preserved due to censoring. On the contrary, if the censoring is not informative, then the loss of information is inevitable. The Cramer – Rao efficiency was taken as a criterion for the quality of the assessment, whereas the Fisher information was taken as the criterion for information about the unknown parameter.

Inference on process capability index Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} for a new lifetime distribution

In various applied disciplines, the modeling of continuous data often requires the use of flexible continuous distributions. Meeting this demand calls for the introduction of new continuous distributions that possess desirable characteristics. This paper introduces a new continuous distribution. Several estimators for estimating the unknown parameters of the new distribution are discussed and their efficiency is assessed through Monte Carlo simulations. Furthermore, the process capability index Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} is examined when the underlying distribution is the proposed distribution. The maximum likelihood estimation of the Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} is also studied. The asymptotic confidence interval is also constructed for Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document}. The simulation results indicate that estimators for both the unknown parameters of the new distribution and the Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} provide reasonable results. Some practical analyses are also performed on both the new distribution and the Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document}. The results of the conducted data analysis indicate that the new distribution yields effective outcomes in modeling lifetime data in the literature. Similarly, the data analyses performed for Spmk\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$S_{pmk}$$\\end{document} illustrate that the new distribution can be utilized for process capability indices by quality controllers.

Integrate-and-fire model of disease transmission.

We create an epidemiological susceptible-infected-susceptible model of disease transmission using integrate-and-fire nodes on a network, allowing memory of previous interactions and infections. Agents in the network sum infectious matter from their nearest neighbors at every time step, until they exceed their infection threshold, at which point they "fire" and become infected for as long as the recovery time. The model has memory of previous interactions by tracking the amount of infectious matter carried by agents as well as just binary infected or susceptible states, and the model has memory of previous infections by modeling immunity as increasing the infection threshold after recovery. Creating a simulation of the model on networks with a power-law degree distribution and homogeneous agent parameters, we find a single strain version of the model matches well with the England COVID-19 case data, with a root-mean-squared error of 0.014%. A simulation of a multistrain version of the model (where there is cross-strain immunity) matches well with the influenza strain A and strain B case numbers in Canada, with a root-mean-squared error of 0.002% and 0.0012%, respectively, though due to the coupling in the model, both strains peak in phase. Since the dynamics of the model successfully capture real-life transmission dynamics, we test interventions to study their effect on case numbers, with both quarantining and social gathering restrictions lowering the peak. Since the model has memory, the stricter the intervention, the higher the secondary peak when the restriction is removed, showing that interventions change only the shape of the curves and not the overall number infected in the population.

To the problem of the shielding systems efficiency in constructions of extra-high voltage electrical apparatus

In the article, the authors proposed a method for estimating the electric load parameters to calculate the distribution of the electric field strength of the solid insulating structure of gas-filled high-voltage devices with axial symmetry. This structure consists of a support and insulating busbar filled with SF6 gas as an internal insulating medium. This technique allows to evaluate the parameters of the electrical load (voltage and field strength) depen-ding on the design features of the device and the shielding system used to equalize the electric field. The proposed methodology allows to evaluate the effectiveness of the influence of design parameters of the protection system for gas-filled high-voltage equipment (instrument transformers, arresters, surge arresters, etc.) when designing and improving individual design solutions. The calculation results are in good agreement with the data of experimental studies and statistical information obtained as a result of monitoring the operation of insulating structures, taking into account actual operating conditions and the influence of external factors. The implementation of this technique allows us to take into account the influence of external factors and operational characteristics inherent in instrument transformers and surge suppressors. In the proposed methodology, as an example, we consider a supporting insulating coating that is in operation under the most unfavorable conditions, such as external pollution, moisture and their combination, overvoltage of various origins, etc. The theoretical conclusions are confirmed by the results of calculations using the example of the support-insulating cover of the surge suppressor of the OПН-500 series. A more accurate determination of the effectiveness of the proposed methodology for predicting the field strength distribution parameters under the influence of a shielding system can be achieved by conducting an additional series of calculations and experimental tests of specific insulating structures. Thus, it was concluded that the obtained results can be used to evaluate the external insulation characteristics of both surge suppressors and gas-filled instrument transformers, as well as similar high-voltage equipment of switchgears and transformer substations in conditions of ultra- and transformer substations ultra-high voltages