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The Nadaraya&ndash, Watson kernel estimator is among the most popular nonparameteric regression technique thanks to its simplicity. Its asymptotic bias has been studied by Rosenblatt in 1969 and has been reported in several related literature. However, given its asymptotic nature, it gives no access to a hard bound. The increasing popularity of predictive tools for automated decision-making surges the need for hard (non-probabilistic) guarantees. To alleviate this issue, we propose an upper bound of the bias which holds for finite bandwidths using Lipschitz assumptions and mitigating some of the prerequisites of Rosenblatt&rsquo, s analysis. Our bound has potential applications in fields like surgical robots or self-driving cars, where some hard guarantees on the prediction-error are needed.

Ecologists are interested in modeling the population growth of species in various ecosystems. Specifically, logistic growth arises as a common model for population growth. Studying such growth can assist environmental managers in making better decisions when collecting data. Traditionally, ecological data is recorded on a regular time frequency and is very well-documented. However, sampling can be an expensive process due to available resources, money and time. Limiting sampling makes it challenging to properly track the growth of a population. Thus, this design study proposes an approach to sampling based on the dynamics associated with logistic growth. The proposed method is demonstrated via a simulation study across various theoretical scenarios to evaluate its performance in identifying optimal designs that best estimate the curves. Markov Chain Monte Carlo sampling techniques are implemented to predict the probability of the model parameters using Bayesian inference. The intention of this study is to demonstrate a method that can minimize the amount of time ecologists spend in the field, while maximizing the information provided by the data.

In this paper, we propose the classical and Bayesian regression models for use in conjunction with the inverted Weibull (IW) distribution, there are the inverted Weibull Regression model (IW-Reg) and inverted Weibull Bayesian regression model (IW-BReg). In the proposed models, we suggest the logarithm and identity link functions, while in the Bayesian approach, we use a gamma prior and two loss functions, namely zero-one and modified general entropy (MGE) loss functions. To deal with the outliers in the proposed models, we apply Huber and Tukey’s bisquare (biweight) functions. In addition, we use the iteratively reweighted least squares (IRLS) algorithm to estimate Bayesian regression coefficients. Further, we compare IW-Reg and IW-BReg using some performance criteria, such as Akaike’s information criterion (AIC), deviance (D), and mean squared error (MSE). Finally, we apply the some real datasets collected from Saudi Arabia with the corresponding explanatory variables to the theoretical findings. The Bayesian approach shows better performance compare to the classical approach in terms of the considered performance criteria.

The testing of high-dimensional normality is an important issue and has been intensively studied in the literature, it depends on the variance–covariance matrix of the sample and numerous methods have been proposed to reduce its complexity. Principle component analysis (PCA) has been widely used in high dimensions, since it can project high-dimensional data into a lower-dimensional orthogonal space. The normality of the reduced data can then be evaluated by Jarque–Bera (JB) statistics in each principle direction. We propose a combined test statistic—the summation of one-way JB statistics upon the independence of the principle directions—to test the multivariate normality of data in high dimensions. The performance of the proposed method is illustrated by the empirical power of the simulated normal and non-normal data. Two real data examples show the validity of our proposed method.

The demand elasticity for a product is the basis of its price determination. The ratio in which a product demand will fall with the rise in its price and, vice versa, can be known as demand elasticity. With increasing population and increasing demand for meat, it is important to accurately estimate price and income demand elasticities. This paper used almost ideal demand systems (AIDS) with log linear analogue of the Paasche price index, referred to as the corrected Stone index to model consumer demand system. The study employs the Kalman filter estimation strategy, which is based on state-space models that are applied to linear regressions with stochastically time-varying parameters, to determine the evolution of price and income elasticities of red meat and fish demand for monthly data 1997–2017. Variables stationary is tested with Hegy test. Results show that Price elasticity for fish is elastic. Elasticity results indicate that the two products are strong substitutes. Income elasticity indicated that fish considered to be luxury good.

Expert knowledge elicitation (EKE) aims at obtaining individual representations of experts’ beliefs and render them in the form of probability distributions or functions. In many cases the elicited distributions differ and the challenge in Bayesian inference is then to find ways to reconcile discrepant elicited prior distributions. This paper proposes the parallel analysis of clusters of prior distributions through a hierarchical method for clustering distributions and that can be readily extended to functional data. The proposed method consists of (i) transforming the infinite-dimensional problem into a finite-dimensional one, (ii) using the Hellinger distance to compute the distances between curves and thus (iii) obtaining a hierarchical clustering structure. In a simulation study the proposed method was compared to k-means and agglomerative nesting algorithms and the results showed that the proposed method outperformed those algorithms. Finally, the proposed method is illustrated through an EKE experiment and other functional data sets Refereed/Peer-reviewed

This paper examines the carbon dioxide (CO2) Environmental Kuznets curve (EKC) hypothesis of a balanced panel of 50 middle-income countries over the period 1996–2013 using a dynamic spatial panel data model with country and time-period fixed effects. Using a Bayesian comparison approach, we systematically searched for the most suitable spatial weights matrix describing the spatial arrangement of the countries in the sample. We found substantial spatial dependence effect in CO2 emissions across the sample of middle-income countries, highlighting the influence these countries exert on their neighbors. Besides, the empirical results showed that the relationship between economic growth and CO2 emissions shaped as an inverted-U trajectory. Furthermore, it has been found that trade openness and energy intensity are the main factors on slightly increasing CO2 emissions, while the urbanization contributes to relative decrease in CO2 emissions.

Zaman and Bulut (2018a) developed a class of estimators for a population mean utilising LMS robust regression and supplementary attributes. In this paper, a family of estimators is proposed, based on the adaptation of the estimators presented by Zaman (2019), followed by the introduction of a new family of regression-type estimators utilising robust regression tools (LAD, H-M, LMS, H-MM, Hampel-M, Tukey-M, LTS) and supplementary attributes. The mean square error expressions of the adapted and proposed families are determined through a general formula. The study demonstrates that the adapted class of the Zaman (2019) estimators is in every case more proficient than that of Zaman and Bulut (2018a). In addition, the proposed robust regression estimators based on robust regression tools and supplementary attributes are more efficient than those of Zaman and Bulut (2018a) and Zaman (2019).The theoretical findings are supported by real-life examples.

One of the most obvious features of time-to-event data is the occurrence of censoring. Rarely, if ever, studies are conducted until all participants experience the event of interest. Some participants survive beyond the end of follow-up time, some drop out from the studies for various non-study related reasons. During research planning it is paramount to consider the effect of censoring the follow-up times on the estimates. Herein, we look into the possibility of assessing the loss of information, as measured by the variability of the survival probability estimates under right censoring. We provide the researchers with an easy to use formula to assess the magnitude of variance inflation due to censoring. Additionally, we conducted simulation studies assuming various survival distributions. We conclude that the provided variance inflation estimator can be an accurate practical tool for applied statisticians., Statistica, Vol. 80 No. 4 (2020)

The Standard Generalised Autoregressive Conditionally Heteroskedastic (sGARCH) model and the Functional Generalised Autoregressive Conditionally Heteroskedastic (fGARCH) model were applied to study the volatility of the Autoregressive Fractionally Integrated Moving Average (ARFIMA) model, which is the primary objective of this study. The other goal of this paper is to expand on the researchers’ previous work by examining long memory and volatilities simultaneously, by using the ARFIMA-sGARCH hybrid model and comparing it against the ARFIMA-fGARCH hybrid model. Consequently, the hybrid models were configured with the monthly Brent crude oil price series for the period from January 1979 to July 2019. These datasets were considered as the global economy is currently facing significant challenges resulting from noticeable volatilities, especially in terms of the Brent crude prices, due to the outbreak of COVID-19. To achieve these goals, an R/S analysis was performed and the aggregated variance and the Higuchi methods were applied to test for the presence of long memory in the dataset. Furthermore, four breaks have been detected: in 1986, 1999, 2005, and 2013 using the Bayes information criterion. In the further section of the paper, the Hurst Exponent and Geweke-Porter-Hudak (GPH) methods were used to estimate the values of fractional differences. Thus, some ARFIMA models were identified using AIC (Akaike Information Criterion), BIC (Schwartz Bayesian Information Criterion), AICc (corrected AIC), and the RMSE (Root Mean Squared Error). In result, the following conclusions were reached: the ARFIMA(2,0.3589648,2)-sGARCH(1,1) model and the ARFIMA(2,0.3589648,2)-fGARCH(1,1) model under normal distribution proved to be the best models, demonstrating the smallest values for these criteria. The calculations conducted herein show that the two models are of the same accuracy level in terms of the RMSE value, which equals 0.08808882, and it is this result that distinguishes our study. In conclusion, these models can be used to predict oil prices more accurately than others.

Nowadays, insurance contract reserves for coupled lives are considered jointly, which has a significant influence on the process of determining actuarial reserves. In this paper, conditional survival distributions of life insurance reserves are computed using copulas. Subsequently, the results are compared with an independence case. These calculations are based on selected Archimedean copulas and apply when the ‘death of one individual’ condition exists. The estimation outcome indicates that the insurer reserves calculated by means of Archimedean copulas are far more effective than those resulting from an independence assumption. The study demonstrates that copula-based dependency modelling improves the calculations of reserves made for actuarial purposes.

In this paper, a general class of two-sided lifetime distributions is introduced via odd ratio function, the well-known concept in survival analysis and reliability engineering. Some statistical and reliability properties including survival function, quantiles, moments function, asymptotic and maximum likelihood estimation are provided in a general setting. A special case of this new family is taken up by considering the exponential model as the parent distribution. Some characteristics of this specialized model and also a discussion associated with survival regression are provided. A simulation study is presented to investigate the bias and mean square error of the maximum likelihood estimators. Moreover, two examples of real data sets are studied; point and interval estimations of all parameters are obtained by maximum likelihood and bootstrap (parametric and non-parametric) procedures. Finally, the superiority of the proposed model over some common statistical distributions is shown through the different criteria for model selection including loglikelihood values, Akaike information criterion and Kolmogorov-Smirnov test statistic values., Statistica, Vol. 80 No. 4 (2020)

In a recent paper, Mazucheli et al. (2019) introduced the unit-Gompertz (UG) distribution and studied some of its properties. It is a continuous distribution with bounded support, and hence may be useful for modelling life-time phenomena. We present counter-examples to point out some subtle errors in their work, and subsequently correct them. We also look at some other interesting properties of this new distribution. Further, we also study some important reliability measures and consider some stochastic orderings associated with this new distribution., Statistica, Vol. 80 No. 4 (2020)

In this paper, we present the Cumulative Median Estimation (CUMed) algorithm for robust sufficient dimension reduction. Compared with non-robust competitors, this algorithm performs better when there are outliers present in the data and comparably when outliers are not present. This is demonstrated in simulated and real data experiments.

Dynamics of neural fields are tools used in neurosciences to understand the activities generated by large ensembles of neurons. They are also used in networks analysis and neuroinformatics in particular to model a continuum of neural networks. They are mathematical models that describe the average behavior of these congregations of neurons, which are often in large numbers, even in small cortexes of the brain. Therefore, change of average activity (potential, connectivity, firing rate, etc.) are described using systems of partial different equations. In their continuous or discrete forms, these systems have a rich array of properties, among which is the existence of nontrivial stationary solutions. In this paper, we propose an estimator for nontrivial solutions of dynamical neural fields with a single layer. The estimator is shown to be consistent and a computational algorithm is proposed to help carry out implementation. An illustrations of this consistency is given based on different inputs functions, different kernels, and different pulse emission rate functions.

The distance constrained maximum likelihood procedure (DCML) optimally combines a robust estimator with the maximum likelihood estimator with the purpose of improving its small sample efficiency while preserving a good robustness level. It has been published for the linear model and is now extended to the GLM. Monte Carlo experiments are used to explore the performance of this extension in the Poisson regression case. Several published robust candidates for the DCML are compared, the modified conditional maximum likelihood estimator starting with a very robust minimum density power divergence estimator is selected as the best candidate. It is shown empirically that the DCML remarkably improves its small sample efficiency without loss of robustness. An example using real hospital length of stay data fitted by the negative binomial regression model is discussed.

The extended situational teaching model is a variation of situational teaching, which itself has roots in situational leadership. Application of situational leadership in education requires the teacher to lead students through various stages of the learning process. This paper presents the relationship between performance measures of extended situational teaching and common pedagogical tools in engineering classrooms. These relationships outlined the response of students at different preparation levels to the application of various course components, including classroom activities and out-of-classroom assignments, in respect to task and relationship behaviors. The results of a quantitative survey are presented to support the existence of such a relationship and to demonstrate the effectiveness of the extended situational teaching model. The survey covered 476 engineering students enrolled in nine different courses over a four-year period within the civil engineering program. The statistical analysis of the survey responses proceeded in two stages. The first stage of the analysis evaluates whether the survey tool can resolve meaningful differences between the categories of the situational teaching model, and provides aggregate recommendations for each category. In the second stage of the analysis, the specific instantiation of these categories is broken down according to academic standing (grade point average) and academic level, offering support for an extended situational teaching model. Conclusions discuss the statistical characteristics of the results and correlations between selected pedagogical tools and performance measures.

This paper introduces a methodology to assess the accuracy of engineering estimates in relation to the final project cost. The objective of this assessment is to develop a comprehensive approach towards obtaining a more reliable estimate of the project cost. This approach relies on the review of a synthesis of literature, which provides a basis for determining key components in the estimation of the capital cost of a project. A systematic review of existing data for selected projects was obtained as well. Employed data cover sampled public transportation projects to maintain existing infrastructure within selected geographical location and specified time. Enhanced analysis of existing data through statistical models was employed to indicate potential measures for prevention of errors in the estimate due to uncertainties in the time, cost, and method of construction. The comparison of results with similar findings from past research shows the effectiveness of presented methodologies and opportunities to enhance statistical analyses of bids and engineering estimates. Conclusions enable project managers to address uncertainties in the bidding process and enhance financial sustainability of projects within specific programs.

In this paper, a new five-parameter distribution is proposed using the functionalities of the Kumaraswamy generalized family of distributions and the features of the power Lomax distribution. It is named as Kumaraswamy generalized power Lomax distribution. In a first approach, we derive its main probability and reliability functions, with a visualization of its modeling behavior by considering different parameter combinations. As prime quality, the corresponding hazard rate function is very flexible, it possesses decreasing, increasing and inverted (upside-down) bathtub shapes. Also, decreasing-increasing-decreasing shapes are nicely observed. Some important characteristics of the Kumaraswamy generalized power Lomax distribution are derived, including moments, entropy measures and order statistics. The second approach is statistical. The maximum likelihood estimates of the parameters are described and a brief simulation study shows their effectiveness. Two real data sets are taken to show how the proposed distribution can be applied concretely, parameter estimates are obtained and fitting comparisons are performed with other well-established Lomax based distributions. The Kumaraswamy generalized power Lomax distribution turns out to be best by capturing fine details in the structure of the data considered.

We present the first general formulas for the central and non-central moments of the multinomial distribution, using a combinatorial argument and the factorial moments previously obtained in Mosimann (1962). We use the formulas to give explicit expressions for all the non-central moments up to order 8 and all the central moments up to order 4. These results expand significantly on those in Newcomer (2008) and Newcomer et al. (2008), where the non-central moments were calculated up to order 4., Comment: 9 pages, 0 figures

We consider here the generalization of the Bilal distribution proposed by Abd-Elrahman (2017) by zeroing in on two measures of reliability, R(t) and P, based on type II censoring. We obtain point estimators namely, λ and θ, of the above said distribution, when both parameters of the distribution are unknown. Maximum likelihood estimators (MLEs), Bayes estimators (BEs) and Lindley’s approximation for the Bayes estimators are proposed. By using independent noninformative type of priors for the unknown parameters Bayes estimators are derived. Although the proposed estimators cannot be expressed in closed forms, these can be easily obtained through the use of numerical procedures. The performance of these estimators is studied on the basis of their mean squared error (MSE), computed separately under LINEX loss function (LLF) and squared error loss function (SELF) through Monte-Carlo simulation technique., Statistica, Vol. 80 No. 3 (2020)

An extension of the exponential distribution due toNadarajah and Haghighi referred to as Nadarajah and Haghighi (NH) distribution is an alternative that always provides better fits than the gamma, Weibull, and the generalized exponential distributions whenever the data contains zero values. However, in practice, discrete data is easy to collect as compared to continuous data. Thus, keeping in mind the utility of discrete data, we introduce the discrete analogue of NH distribution. Our main focus is the estimation from the frequentist point of view of the unknown parameters along with deriving some mathematical properties of the new model. We briefly describe different frequentist approaches, namely, maximum likelihood, percentile based, least squares, weighted least squares, maximum product of spacings, Cramèr-von-Mises, Anderson-Darling, and right-tail Anderson-Darling estimators, and compare them using extensive numerical simulations. Monte Carlo simulations are performed to compare the performances of the proposed methods of estimation for both small and large samples. The potentiality of the distribution is analyzed by means of two real data sets., Statistica, Vol. 80 No. 3 (2020)

Liu (2007) discussed a new measure, known as the information volatility function to study the variability of the uncertainty contained in a probability distribution. In the present paper, we extend this concept to the residual random variable, a dynamic information volatility function and study its usefulness in reliability modelling. Different ageing and characterization properties of dynamic information volatility function are also derived., Statistica, Vol. 80 No. 3 (2020)

Heavy-tailed distributions are often encountered in economics, finance, biology, telecommunications, geology, etc. The heaviness of a tail is measured by a tail index. Numerous methods for tail index estimation have been proposed. This paper reviews more than one hundred Pareto (and equivalent) tail index estimators. It focuses on univariate estimators for non-truncated data. We discuss the basic features of these estimators and provide their analytical expressions. As samples from heavy-tailed distributions are often analysed by researchers from various sciences, the paper provides nontechnical explanations of the methods, so as to be understood by researchers with intermediate skills in statistics. We also discuss the strengths and weaknesses of the estimators, if known. The main focus of the paper is semi-parametric estimators; however, a number of parametric estimators under-represented in previous reviews are also discussed. The paper can be viewed as a catalog or a reference work on Pareto-tail index estimators. A Monte-Carlo comparison of more than 90 estimators is presented., Statistica, Vol. 80 No. 3 (2020)

У статті зосереджено увагу на поняттях «цифровізація» та «глобалізація». Визначено основні тенденції глобалізаційних процесів, їх позитивні та негативні наслідки для суспільства. Охарактеризовано блоки цифровізаційної екосистеми. Визначено, що ті масиви даних, які наразі існують є двигуном інновацій та виступають новими, альтернативними джерелами статистичних даних для офіційної статистики. З метою усвідомлення ієрархії даних, розроблено організацію великих даних. З’ясовано, що незважаючи на усі ризики, глобалізація відкриває нові можливості для розвитку освіти, науки, медицини. розвиваючись в глобалізаційних умовах, країнам необхідно діяти консолідовано, з метою подолання глобальних проблем. Таким чином, наукова розвідка сучасного стану цифровізаційних процесів в умовах глобалізації 4.0, стали основною метою написання цієї роботи.

The article examines the dynamics of the number of registered unemployed and unemployed in the definition of the International Labor Organization (ILO), as well as the levels of these indicators. It is determined that compared to 2010, the largest increase in the number of registered unemployed could be observed in 2011. The most significant decrease in the studied indicator during the entire research period, both compared to 2010 and the previous year, was in 2017. In 2018–2019, the number of registered unemployed continued to decline. The increase in the registered unemployment rate compared to 2010 was in 2011, 2013–2016, and a significant increase in the level of the studied indicator was recorded in 2015. The decrease in the studied indicator was recorded in 2012 compared to 2011, as well as in the last four years of the research period. The unemployment rates by the ILO methodology are most informative figures on the unemployment in Ukraine. The number of unemployed in 2010–2019 did not have a clear trend and depended on the socio-economic situation in Ukraine: compared to previous periods, the indicator decreased in 2011–2013, and in 2014 increased rapidly, due to the difficult socio-political situation in the country, which had adverse effects for the economic situation; in 2015, the average number of unemployed decreased both compared to the previous year and to 2010. However, in 2016–2017, the studied indicator began to grow gradually, but did not reach the level of 2010, and decreased in 2018 and 2019 both compared to the previous period and to 2010. Analysis of the intensity of the dynamics of the unemployment rate of the population aged 15–70 years by the ILO methodology showed that throughout the ten-year research period this indicator in Ukraine decreased in 2011–2013 and increased in 2014–2018 compared to 2010, and in 2019 it decreased to the level of 2010. The sex-age structure of the unemployed is analyzed, its features are revealed and the generalized age characteristics of the unemployed are determined. In contrast to the registered unemployment, which indicates the predominance of women among the unemployed, a sample survey allows to suggest that Ukraine is characterized by “male” unemployment. Among the unemployed, the largest share was accounted by young people aged 15–34. The highest unemployment rate among young people aged 15 to 24 was due to the fact that without proper education and professional experience, young people were not able to compete on equal terms on the labor market. The average age of the unemployed in Ukraine in 2019 compared to 2010 increased by four years, including almost four years for men and five years for women. Because this indicator cannot be used as a generalization due to the heterogeneity of the population, as evidenced by the indicators of variation, mode and median, which are the structural averages, are the most suitable for the generalization of the characteristics of the unemployed by age. The structure of the unemployed by cause of unemployment was studied, with assessing the structural change. It is established that during the studied period in Ukraine this structure was changed significantly, as evidenced by the root mean square coefficient of structural change.

The balanced environmentally sustainable economic development of Ukraine can be achieved by increasing the efficiency of the nature protection efforts, which requires the improved methods for assessment, modeling and forecasting of environmental performance and environmental pollution indicators. The article’s objective is to make a statistical forecasting of environmental pollution indicators in Ukraine, to outline the areas of nature protection work in this country. Air pollution, water pollution and hazardous wastes in Ukraine are forecasted considering the main factors of influence, selected with reference to the Strategy of the State Environmental Policy of Ukraine: GDP, the number of implemented resource-saving technologies, energy intensity of GDP, current spending on environmental protection. The project estimates for air pollution, water pollution and hazardous wastes were derived by use of regression models and factors projection. Results of the forecasting show that the emission of pollutants and carbon dioxide in the air, water pollution and pollution with hazardous wastes will be significantly reduced by 2022 if the current trends and patterns of development remain unchanged. Results of the forecasting confirm the need to introduce a series of measures concerned with waste treatment, air pollution and water pollution, to improve the regulatory system in nature protection activities in Ukraine.

The problems of valuating and recording the value of innovation objects in the system of accounting and reporting are investigated. It is argued that one of the factors hindering the development of innovation is insufficient information support covering a set of primary and consolidated data, the organization of storage of accumulated information and methods of its presentation and transformation. The main valuation models used by business entities to include the value of innovation objects in the economic transactions are identified. It is established that the commercial use of innovation objects requires calculation of market or other value. The main methodological approaches to valuation of innovation objects and their impact on the formation of the value of innovation objects are proposed, taking into account these objects’ characteristics, specifics of the economic activities in which they are exploited, and availability of information on a group of objects, which determines the choice of appropriate valuation approach. The ways of valuating innovation objects at company level are highlighted. Methodological approaches to recording business transactions with innovation objects in the accounting and reporting system are elaborated, which will contribute in the sound assessment of innovation objects and their correct recording in the accounting system of a business entity and ensure effective management of innovation.

The cumulative potential of the sustainable innovation-driven development of the regions of the Republic of Belarus is proposed to be estimated by measuring individual sub-potentials (social, demographic, environmental-economic, investment) and subsequent modeling of the aggregate characteristics for each of the regions. It is argued that the health of the population is an important component of the social sub-potential and the necessary condition for the development of all other sub-potentials. Statistical assessment of health within the framework of the system of indicators of innovation-driven sustainable development of regions is proposed to be carried out using core indicators such as life potential and healthy life expectancy of the population. The article is devoted to a study of health in the regions of Belarus on the basis of healthy life expectancy (HLE), which reflects the average number of years lived by the population, taking into account their health status (as a rule, measured on the basis of representative surveys). That is, it is life expectancy estimated with account to the quality of the years lived. It allows to estimate the loss in life expectancy due to the deteriorating health. The article provides a statistical assessment and analysis of HLE dynamics for the population of Belarus at birth (and for specific ages) for 2005-2018. HLE in Belarusian regions are analyzed using Sallivan’s method. The healthy life expectancy of Belarusians at birth in 2018 was 68.09 years and increased by more than 10% (or 6.49 years) compared to 2005, with an increase occurred in each of the studied ages. It was revealed that although Belarusian women lived longer, they tended to give a lower life quality assessment than men (due to “poor” health). The gap between HLEs of men and women in 2018 was 6.78 years: women’s healthy life expectancy was 71.38 years, men’s – 64.60 years. At the same time, the loss in life expectancy resulting from poor health was 4.64 years for men and 7.98 years for women. Brest region and Minsk were the leaders in terms of HLE (both in 2015 and in 2018), Vitebsk and Minsk regions were among the outsiders in 2015 and Mogilev and Minsk regions – in 2018. At the next phase, the estimated indicators, together with the indicator of life potential of the regions, will be used as the basis for assessing the population’s health as part of the social sub-potential of the country regions.

The automotive sector is one of the leading industries in Turkey, and therefore worthy of examination, both in terms of its size and its economic impact. The Turkish automotive sector can be divided into the sale of new vehicles and their resale as used vehicles. It is notable that the used vehicle market in Turkey is economically more significant, hence the current study’s focus is on Turkey’s used vehicle market. According to the study’s findings, which aims to analyze the used vehicle market in the context of consumer demographics through ordinary least squares and quantile regression method and data obtained from the Turkish Statistics Institution (TURKSTAT), meaningful segments related to demographic characteristics such as income and education level were reached.

This study aims to contribute to the national statistical glossary compilation, namely a glossary supporting the Generic Statistical Business Process Model (GSBPM). The GSBPM is a standard framework that allows statistical authorities to use corporate and harmonized terminology for the statistical business process. In Ukraine, the implementation of the GSBPM in statistical practice puts forward the need for its terminological support. The glossary is a means of understanding among statisticians and contributes to professional vocabulary formation. Statistical terminology today creates an independent terminological system. The system nature of statistical language is related to the professional limits and the interdependence of phenomena within these limits. As a subsystem of the general statistical system, the GSBPM has its vocabulary. We argue a complex, non-linear, and dynamic interrelation between statistical business processes in the GSBPM. The business processes form some synergy and involve professional vocabulary for different business phases, implying a non-mechanical approach to glossary compilation. According to studied international practice, there is no single approach to statistical glossaries construction and presentation. The choice of basiс international standards is crucial to ensure the GSBPM methodology and quality. We formulated several experience-based requirements and principles for the GSBPM glossary. Identified problematic issues may be useful for further work on statistical terminology. The progress in official statistics, both international and national, significantly affects this work's qualitative aspects. An essential factor in bringing national statistical language closer to international standards is undoubtedly the dialogue between the academic community and statisticians-practitioners. The development of glossaries for the General Activity Model for Statistical Organizations (GAMSO) and the Generic Statistical Information Model (GSIM) is outlined as a prospective area of further studies.

The focus of paper is on explaining variations in wage earning potential of regular wage earners caused by varying skill levels. Further, the paper attempts to analyse the conditional causal effect for a broad range of occupational groups to infuse external validity during estimation process which helps to explore how universal is the causal effect. The study brought out the fact that skill level of workers affects the wage-earning potential of workers significantly. However, different skill requirements to perform a range of tasks & operations, along with associated complexity, moderates the strength of causal linear relationship and the resultant slope indicating relationship between skill level of workers and their wage-earning potential varies significantly across occupational groups. Thus, conceptualization of task-content based approach of occupations determines wage-earning potential of workers and hereby is a promising boulevard for future research. The study recommends in job training courses along with introduction of intra-occupational diversified range of tasks & operations to secure incremental wage.

The paper deals with well-being of employees who invest heavier in work. The main aim of the present study was to examine relationship between workaholism and work enjoyment as part of the work engagement. Paper focuses on workaholics and their emotional experience in performing work (affective component of well-being). The unique method based on time diary, including data on happiness, was used. Results suggest that non-workaholics feel happier when performing paid work than workaholics. Gender and education are significant background predictors influencing heavy time investment, while parenthood and place of living do not correlate with time workaholism. Men-workaholics work longer than women-workaholics, with no significant difference in happiness. Women-workaholics feel happier when performing unpaid household work, but men-workaholics enjoy more time with children. Education in relation to income, time investment and happiness indicate that workaholism in Slovakia exists in a forced form in order to achieve the required income and forced heavy time investment must undertake deeper analysis.

Information and analytical database for the market support is required to prevent communications of contradictory information to higher levels of management, with adverse effects for the process of taking rational management decisions. The article’s objective is to substantiate the information and analytical support for studies of the logistics services market, with constructing a system of statistical indicators for this market assessment, to be laid as the solid basis for elaborating medium-term and long-term strategies and policies of the logistics services market in Ukraine. A definition of information and analytical support for studies of the logistics services market is given; a review of secondary sources of data for this market studies is made. A conceptual model for information and analytical studies of the logistics services market is proposed. The key statistical indicators for studies of this market are identified, with substantiating the feasibility of their use in computing multivariate indicators for the assessment of performance and capacities of the logistics services market in Ukraine. The core criteria to be met by the abovementioned system of statistical indicators are highlighted. A system of statistical indicators for the assessment of the logistics services market is proposed, containing four modules. It allows for diagnosis of this market performance and tendencies, with accounting for the impact of other related markets and activities, and for forecasting. This system, constructed with consideration to the global practice, is designed for comprehensive studies of the logistics services market.

We estimate the effect of an electricity tax on aggregate electricity consumption with the synthetic control method. The tax was introduced in the Swiss city of Basel in 1999 and, together with other tariff changes, increased marginal electricity prices by 5.4–8.0%. We compare the actual and a hypothetical electricity consumption in the years 1999–2006. The latter is a weighted average of electricity consumption in other Swiss cities and captures the hypothetical situation without the tax. We find a statistically insignificant effect of the tax increase of − 2.7 to − 1.9%, which implies a rather small, but not unreasonable, price elasticity of between − 0.5 and − 0.2. Ambiguous effects on average prices and an unfortunate communication by officials may explain why the innovative reform failed to induce a stronger response., Swiss Journal of Economics and Statistics, 156 (1), ISSN:0303-9692, ISSN:2235-6282

QS World University Rankings is one of the most prestigious rankings showing the effectiveness of the institutions of higher education in comparison to others. The scientometric citation rate that determines one-fifth of the final score is quite important in this ranking and is considered an indicator of the quality of the teaching staff. With this in mind, the main problem of the article is to study the tendencies of citations for the research and teaching staff from Ukrainian universities, to ensure entry for more Ukrainian universities into this ranking. The problem is a topical one, as there seems to be no detailed scientific analysis devoted to indexing and citing the works of the Ukrainian scientists, published in scientometric databases recognized by the Ministry of Education and Science of Ukraine. To solve the problem, mathematical and statistical methods were used in analyzing the publication activity of researchers from Ukrainian universities. For construction of prognostic models of the tendencies in the publication activity of the research and teaching staff from higher educational institutions of Ukraine, the method of exponential smoothing according to the Holt model was used, which showed the best consistency indicators for the empirical data and the obtained theoretical models. To analyze the publication activity of Ukrainian universities from the perspective of the QS rating methodology, the universities were selected using the authors’ methods. Results of the study allowed the authors to determine the peculiarities of the dynamics of publication activity of research and teaching staff from Ukrainian universities over the last 9 years. The main peculiarity was the accelerating growth of citations of Ukrainian research and teaching staff from the moment of reorientation to the European experience in research and education, with the resulting change in the terms of performing education activities, effected by Cabinet of Ministers of Ukraine. In addition, forecasting of citation indexes of scientific papers by researchers from higher educational institutions of Ukraine in 2021–2023, which are taken into account in the 5th part of the calculation of QS rating by its method (normalized number of citations received by university articles for 5 years according to the Scopus database per 1 teacher), shows that this indicator is a very serious problem for Ukrainian universities in the context of competition with foreign universities. For its solution, measures should be developed both at the government level and at the level of higher education institutions of Ukraine to effectively support the publication activity of the university research.

The requirements to implementation of financial monitoring by auditing entities, as specified by the Law of Ukraine “On prevention and counteraction to legalization (laundering) of proceeds from crime, financing of terrorism and financing of proliferation of weapons of mass destruction” from 06.12.2019 No 361-ІХ, enforced on 28.04.2020, are analyzed. The existence of unclear interpretations of some notions in the this Law of Ukraine or heavy financial sanctions that may be imposed on auditing entities call for elaboration and introduction of internal firm documents concerned with financial monitoring. While in the previous edition of the above Law of Ukraine the features of financial monitoring organization were specified for auditing entities in case of rendering certain categories of services to a client (realty transactions; asset management; raising funds to establish legal entities, support to their operation and management, buying and selling of corporate rights), they are not found in the updated edition of this Law of Ukraine. Therefore, auditing entities need to rely upon general norms of the Law of Ukraine in organizing financial monitoring. A series of administrative documents were elaborated for this purpose: the order on assignment of a person responsible for carrying out financial monitoring; the conclusion of business character test for the candidate on the position of the responsible person, the Rules for financial monitoring of an auditing entity, and the monthly fact sheet of the responsible person about the results of carried out measures on financial monitoring. The developed Rules of financial monitoring cover all the regulatory requirements for the implementation of financial monitoring, with the possibility of making change in case of need. The Rules must be informed to the staff of an auditing entity, engaged in rendering auditing and non-auditing services, through the involvement in internal training on financial monitoring issues. Apart from the Rules, it is proposed to supplement the working documents supporting the financial monitoring procedures by the following sections: (i) “Documentary support to financial monitoring of auditing entities”; (ii) “Personnel and personnel training on financial monitoring issues”; (iii) “Documentary support to interactions with the State Service of Financial Monitoring of Ukraine, ministries and administrative departments”, which are supposed to help auditing entities to fully observe the regulatory requirements and avoid heavy financial sanctions on the part of controlling and regulatory bodies.

It is demonstrated that the domestic agricultural sector continues to be underfunded in spite of special lending programs for agricultural producers implemented by banks and stimuli provided by international financial organizations to agricultural producers to make them introduce energy saving measures. The research objective is to review the current situation with bank lending of the agricultural sector in Ukraine and determine its main problems and prospects. The following research methods were used: induction, deduction, system approach, statistical analysis, logical generalization, graphical method. It is shown that the bank lending in Ukraine is operating now under the pressures of the financial globalization processes and in the post-crisis condition of the bank sector, high risks and information asymmetry characterized by lack of complete and reliable information about the factors underlying business operation in various economic sectors, required for the assessment of the borrowers’ creditworthiness, and by inefficient financial and credit instruments. A review of global practices shows that in most part of foreign countries governments support lending to agricultural producers through budget preferences or limitations imposed on the banks that can lend agricultural producers, with laying down a requirement that the loans provided to the agricultural sector must be the cheapest ones. Lending of agricultural producers in European countries is most often carried out by cooperative banks, with mortgage of lands being the main form of long-term lending. Considering the European practice, creating a specialized agrarian bank or applying economic stimuli to banks engaged in lending of the agricultural sector may be a solution of lending problems in Ukraine. The study of specific features of bank lending to the agricultural sector at the current phase of economic development in Ukraine confirms the need for further with scientific justifications of the government support to lending processes in the agricultural sector.

In the context of global challenges of today, an important objective is raising the society’s awareness of the main socio-economic indicators. The most significant of them are indicators of demography statistics, characterizing the number of population and the quality of life, and laying the methodological basis for macroeconomic comparisons. The purpose of the study is to determine current trends in the indicators of Ukrainian population; formulate proposals for solutions of problems related with organization of sample surveys and the All-Ukrainian census. Abstract-logical and monographic methods, theoretical generalization, tabular and graphic methods, economic-statistical methods are used in the study. The source of information for a description of current demographic processes is data of the State Statistics Service of Ukraine. The authors analyze the indicators of the number of permanent and actual population in 1995-2020, its natural and migratory movements using a set of absolute, relative and average statistical indicators of dynamics. A comparative analysis of national censuses in Ukraine and neighboring European countries was performed. Groups of statistical and demographic indicators, which are formed in the regions, analyzed in time of census and characterize current demographic processes at regional and national level, were distinguished. An organizational chart for performing the All-Ukrainian census with engaging the administrations of consolidated territorial communities is elaborated. A partnership model of the All-Ukrainian Census is proposed, which is based on the cooperation of the State Statistics Service of Ukraine, ministries and agencies; it shows the main phases in organizing and performing the census in the country, and involves a network of consolidated territorial communities of Ukraine and information bases in the regions. Further studies are expected to focus on elaborating mechanisms of the proposed partnership model for the All-Ukrainian census by case of Zhytomyr region.

The external control over the quality of audit is exercised in Ukraine due to the requirement of the specialized law, in spite of the missing definition of the quality of audit and its criteria in domestic and international normative documents. The article’s objective is to draw attention to the issue of the quality of audit by elaborating on its dual nature, terms and principles for organization of control over business results of auditing entities and user expectations concerning these results. For this purpose, the quality of audit is addressed from two dimensions: external and internal. The external dimension of the quality of audit is analyzed in terms of expectations concerning the quality of audit, held by users of audit results (official regulatory bodies of bank, financial and corporate relations; official fiscal bodies and controlling bodies of public supervision over auditors; actual owners of businesses; hired management) and the coincidence between these expectations and actual results of audit. The internal dimension of the quality of audit is analyzed in terms of auditing entities and their expectations from the categories of entities such as customers, owners of customers, controlling bodies, personnel of auditing entities or invited external auditors or experts. Distinctive features of the Ukrainian market of audit services are highlighted, prevalence of supply over demand in the first place. Questions are posed which need to be responded for proper organization of control over the quality of audit: Is control over the quality of audit is necessary? If “yes”, then to whom? Do formalized expectations of users of audit results concerning the quality of its result really exist? If audit is a type of control over the quality of reporting and management on the whole, would it be expedient to set up control over the controller? What is the essential meaning of effectiveness and performance of control over the quality of audit, especially external one? Can positive results of the external inspection of auditing entities to the effect of the quality of audit be regarded as “indulgence” for a certain period, or the permanent external control is needed after all? Should control over the quality of audit be obligatory only for the auditing entities involved in inspections of entities of public interest, or should it cover all the auditing entities without exception? The analysis gave grounds to the author to ask if it would be more expedient in the Ukrainian realities that the term “quality of auditing” was abandoned and replaced by the term “compliance with the standards”.

The OECD’s Development Assistance Committee (DAC) has compiled foreign aid statistics since the 1960s, and it invented the concept of Official Development Assistance (ODA) in 1969. For decades, ODA data were on actual flows, the DAC having rejected suggestions commencing in 1963 to instead focus on flows’ “grant equivalents”. But in 2014 the DAC decided, from 2018, to switch ODA loan reporting to “grant equivalents” using unrealistic parameters that exaggerated donors’ fiscal effort. In 2016 it decided to abandon the requirement that all ODA transactions be concessional. By 2018, having failed to agree grant equivalent methodology for equity investments, loans to the private sector, and debt relief, it decided to maintain reporting of these on a flow basis. ODA therefore now mixes flows and grant equivalents, which are incommensurable statistical quantities, and embodies other contradictions and anomalies. This paper examines the degradation of the ODA measure and identifies general lessons for statistical development exercises and quality control efforts.

The paper contains a comparative analysis of the possibilities of using different software products to solve the problem of missing data on the example of the sample for which different variants of data skips are simulated. The study provided an opportunity to identify the strengths and weaknesses of these software products, as well as to determine the effectiveness of a particular method for different amounts of missed information. Thus, the easiest way to handle the situation with missing data is Statistica, but there are offered only simple methods of processing data with missing values in Statistica. So, this program will help to cope with the missed data when there is a small number of omissions (up to 10%). SPSS offers a wider range of data imputation methods than Statistica, and at the same time it offers a more user-friendly interface compared to the R or SAS programming language. In the R and SAS software environments, you can use different methods of missing data imputation from the simplest to the most complex, such as, for example, multiple imputation. Thus, R and SAS are the most powerful missing data recovery programs, but they are more complex for users because they require knowledge of the programming language. It is found out that none of the mentioned software-analytical environments has built-in procedures for processing categorical data with missing values. There are approaches that can be implemented by analogy for ordered categories in R and SAS software environments, but it does not cover all the needs of the analysis of research, which are implemented in the form of surveys with the results that are mostly presented as answers. The methods used to impute quantitative data cannot be applied to categorical data, even if numbers are used to encode responses. The study undoubtedly proved that handling the missing data, as well as the choosing of possible ways to use certain methods of data imputation in different software environments should be approached very carefully and the problem of imputation should be solved in each case based on careful analysis of the existing database, considering not only the characteristics of the data and the number of gaps, but also the specific of a particular study. Dealing with missing data involves a wide range of the issues, which includes both the exploration of the nature of gaps, the methodology for data processing and imputation, depending not only on their nature but also on the type and the use of various software environments on missing data imputation. It is planned in future research to assess the effectiveness of the recoverability of imputation methods in different software environments, as well as to develop methodological principles for restoring gaps for categorical data and implement them into practice.

The development of business can stuck in a series of problems related with market expansion, recruiting of staff in the dealer network, setting interaction channels etc. These can be dealt with by new economic mechanisms like franchising that allows for increasing the effectiveness of small business. But each of its type has advantages and shortcomings, which, if misunderstood, can cause serious risks to the operation of each partner and business on the whole. The article’s objective is to investigate criteria for classifi cation of franchising and business specifi cs of its types. It is shown that franchising can take various types and forms in business operation, depending on the classifi cation criteria. A detailed discussion of franchising types is given, classifi ed by character of business operation, opportunities and intentions of franchisee, strategy for franchising business expansion, number of franchising enterprises owned by one franchisee, value of franchise, existence of intermediaries between franchiser and franchisee. It is argued that the above given classifi cation allows one to position franchising types in business operation, choose the most appropriate type of franchising or a type of interactions with partners in creating a franchising enterprise, make projections for franchising-based businesses. It is emphasized that franchising is not an all-purpose tool for addressing all the problems of small business; it has a great many shortcomings that may be caused by possible dishonesty of a franchiser or rooted in the very nature of franchising. Two groups of shortcomings specifi c to franchising are discussed in detail. Advantages of the franchising system are demonstrated by comparing statistical data about the fi rms operated on franchising terms and by traditional methods; by highlighting the signifi cant role of a ready-made standardized business plan provided by a franchiser to a franchisee, which helps insure the latter from business risks; and easy access of an entrepreneur deciding to launch own business (i. e. a franchisee) to bank loans. В статті досліджено критерії класифікації франчайзингу. Визначено, що залежно від них франчайзинг набуває різноманітних видів і форм у підприємницькій діяльності. Виявлено, що кожен із різновидів франчайзингу має певні особливості, переваги та недоліки, і вибір конкретної форми визначатиметься стратегією правовласника, умовами ринку, специфікою діяльності, ресурсами та багатьма іншими факторами. Доведено, що класифікація франчайзингу дозволяє: визначити роль і місце різновидів франчайзингу в підприємницькій діяльності; цілеспрямовано обрати найбільш ефективну форму або вид взаємин із кожним окремим партнером при створенні франчайзингового підприємства; здійснювати прогнозну оцінку розвитку франчайзингової діяльності.

A specific feature of Ukraine is a significant regional differentiation of the population by the standard of living. Integrated assessment of the standard of living in Ukrainian regions will enable to explore this standard by one indicator. This technique will allow not only to carry out a rating assessment of the regions on permanent basis but also to monitor dynamic change in the situation in each region, with determining the impact of individual factors on the resulting indicator. The study’s database was official statistical information. The study’s methods were index analysis, statistical groupings and relative indicators. On the basis of a review of methodological approaches to the standard of living assessment, the author proposes to use the regional index of living standard, with account to methodological recommendations for its calculation, related with the changed socio-economic situation in the country and the respective amendments in the statistical observation methodology. The research methodology interprets the standard of living as a combination of three components: financial status, living conditions and the social environment performance. Each of these aspects is characterized by a set of factors which is very outdated in the current methodological guidelines and needs to be reviewed. Therefore, the author proposed and theoretically substantiated a set of factors that most adequately reflects the actual standard of living of the Ukrainian population. The calculation of the regional standard of living covers four consecutive phases. A set of indicators of financial status, living conditions as a whole and by socio-demographic group is formed at the first phase, with making analysis of the social environment performance. Standardization of the selected indicators is made at the second phase. The third phase involves calculation of weights and integrated standard of living indicators for each constructed module. The regional index of standard of living is calculated at the fourth phase. The calculated regional indexes should be used in developing regional programs to improve the standard of living and in the predictive estimates of the population’s life potential in the medium term.

To ensure the competitiveness in world markets in the context of deepening globalization processes, Ukraine needs to adjust its own raw material base, which will qualitatively change the structure of Ukrainian exports from raw materials to goods with a high share of value added. The purpose of the article is to assess the development potential of chemical, textile, agro-processing and woodworking industries of Ukraine on the basis of import substitution and export orientation, and to substantiate organizational and economic forms of its practical implementation. The authors propose an interpretation of the term “industrial system development potential”. The peculiarities of operation of the manufacturing industry in Ukraine are determined on the basis of a comparative assessment of the density of cross-sectoral links, the cost and innovation level of domestic and European chemical, textile, woodworking and agro-processing industries. Based on the results of the analysis of the technological profile, the level of capacity utilization and performance indicators of the largest chemical enterprises of Ukraine, the strategic guidelines for the development of promising chemical industries are substantiated and organizational and economic forms of realizing their potential are proposed, in particular in the Western region. Proposals for ensuring competitive conditions for participants in the domestic market of light industry products are provided, the need for simplified regulatory procedures and investment incentives to ensure the development of domestic light industry enterprises is substantiated. An organizational mechanism for restoring the raw material base of textile and other industries is developed. The regions of Ukraine are grouped according to the potential of timber harvesting and industrial processing. The perspective directions for the woodworking industry development in the administrative-territorial units of the Western region are defined (by production type), and the basic strategies of their realization, focused on the internal and external markets, are outlined. A comprehensive review of operation problems of agro-processing productions in Ukraine is made through the prism of their resourcing from a regional perspective. The key problems are outlined and the prospects for the development of grain, meat and milk productions are substantiated, based on current and forecasted trends in the respective commodity markets. Organizational forms for realization of the development potential of agro-processing productions in Ukraine and mechanisms for their institutional support are proposed.

Univariate normality tests are typically classified into tests based on empirical distribution, moments, regression and correlation, and other. In this paper, power comparisons of nine normality tests based on measures of moments via the Monte Carlo simulations is extensively examined. The effects on power of the sample size, significance level, and on a number of alternative distributions are investigated. None of the considered tests proved uniformly most powerful for all types of alternative distributions. However, the most powerful tests for different shape departures from normality (symmetric short-tailed, symmetric long-tailed or asymmetric) are indicated.

Using various administrative and statistical electronic registers when carrying out population or housing censuses is becoming the increasingly applicable technology for obtaining statistical and demographic information required for taking sound and timely solutions at central government, region and territorial community level. This issue has been in the increasingly stronger focus of international organizations (such as UN Population Fund, UN Economic Commission for Europe, Eurostat), statistical offices of most advanced countries and individual researchers. But the available methodological documents and publications, especially ones of national researchers, give grounds for the conclusion that this issue needs in-depth studies for the implementation in the statistical practice. The article’s objective is to sum up international experiences in using electronic register systems for population and housing censuses in European countries, for their due accounting in Ukrainian realities. The EU legislation is given, recommendations of international organizations on carrying out a census on register basis are analyzed, with emphasis made on the need to introduce unique identifiers for authentification of units and linking of registers. Experiences of using register systems for census purposes are studied and summarized by investigating the cases of two European countries: Finland and Estonia. It is stressed that Estonia that started to actively use registers for public and government needs only at the beginning of this millennium is able to quickly catch up with Finland carrying out census on register basis over several decades. Experiences of developed countries can be useful for Ukrainian statisticians when organizing next population censuses. The forthcoming census will not yet be based on register information, but if a register system is designed, a sound demographic register and a register of addresses (buildings and housings) in particular, and a methodologically grounded plan for gradual implementation of registers for obtaining necessary information about the population is elaborated, this objective will be feasible.

Continuous distribution of variables under study and auxiliary variables are considered. The purpose of the paper is to estimate the mean of the variable under study using a sampling design which is dependent on the observation of a continuous auxiliary variable in the whole population. Auxiliary variable values observed in this population allow to estimate the inclusion density function of the sampling design. The variance of the continuous version of the Horvitz-Thompson estimator under the proposed sampling design is compared with the variance of the mean of a simple random sample. The accuracy of the estimation strategies is analysed by means of simulation experiments.

This study uses trade data from Switzerland’s Federal Customs Administration to examine the impact ofCovid-19 on international goods trade between January and July 2020. We show that Swiss trade during that period fell by 11% compared to 2019 and that the contraction following the “Federal Lockdown” in mid-March was considerably steeper than the Swiss trade collapse in the aftermath of the Lehman Brothers bankruptcy in September 2008. Examining cross-country variation inCovid-19 cases, the stringency of containment measures, and Swiss trade flows, we document that the pandemic adversely affected both the demand and supply side of foreign trade, while trade restrictions and exchange rate fluctuations played no major role behind the rapid decline of Swiss trade in the first half of 2020.

Single sampling inspection plans when the remainder of rejected lots is inspected with given Average Outgoing Quality Limit (denoted AOQL) minimizing mean inspection cost per lot of process average quality are presented in this paper. These plans were introduced by Dodge and Romig for inspection by attributes (each inspected item is classified as either good or defective). The corresponding plans for inspection by variables were created by the author of this paper. The comparison of these two types single sampling inspection plans from the economic point of view and the comparison of their operating characteristics (producer’s risk, consumer’s risk) is performed in present paper. We shall also show how the decision problem (inspection by variables or inspection by attributes) can be solved in practice using software Mathematica.