Determination of the minimum number of periods for assessing the sustainable development indices of the EU countries using the methods of ordinal statistics
DOI:
https://doi.org/10.30837/ITSSI.2024.27.215Keywords:
law of distribution; quantity of assessment periods; statistical information; identification; mathematical expectation; ordinal statistics; dispersion; index of sustainable development.Abstract
The subject matter of the article is the process of assessing the sustainable development indices of the European Union countries. The goal of the article is to develop a methodology for determining the number of periods for which it is necessary and sufficient to assess the sustainable development indices of states. The article results the following task: to develop a methodology for determining the law of distribution of random variables of sustainable development indices. Determination of the minimum number of periods for assessing the sustainable development indices of the European Union countries. Methods used: parametric and ordinal statistics. The following results are obtained: parametric and non-parametric methods of statistics, their advantages and disadvantages are considered. Various methods of estimating the distribution function for small samples, in particular the method of rectangular contributions and the method of uncertainty reduction are analysed. Particular attention is paid to the problem of changing the law of scattering of quality indicators when changing the conditions of technology. A graph-analytical method for identifying the law of distribution of random variables based on a small amount of statistical information is proposed. For this purpose, the theory of ordinal statistics was used. A step-by-step methodology for identifying the law of distribution of random variables using 10 ordered values has been developed. The mathematical expectations of ordinal statistics for three distribution laws are proposed. A methodology for determining the number of periods for assessing the indices of sustainable development of countries using ordinal statistics is developed. The study is based on the analysis of statistical data for the last ten years and their ordering in ascending order. The mathematical expectations of ordinal statistics are used to select appropriate distribution laws. Given the limited information available when working with small samples, the article proposes a methodology that allows obtaining the maximum amount of information from the available data. The developed approach makes it possible to take into account the uncertainty of the phenomenon under study and make informed decisions based on statistical analysis. Conclusions: based on the knowledge of the law of distribution, a methodology for determining the minimum number of periods for assessing the sustainable development indices of the European Union countries is proposed. Testing of the methodology on real numerical data has confirmed that the minimum number of periods is seven, provided that the distribution law follows the normal law.
References
Список літератури
Liu Y., Huang B., Guo, H. A big data approach to assess progress towards Sustainable Development Goals for cities of varying sizes. Commun Earth Environ. 2023. №4 (66). DOI: https://doi.org/10.1038/s43247-023-00730-8
Xu Z., Chau S. N., Chen X. Assessing progress towards sustainable development over space and time. Nature. № 577. 2020. P. 74–78. DOI: https://doi.org/10.1038/s41586-019-1846-3
Yali L. et al. Evenness is important in assessing progress towards sustainable development goals, National Science Review. 2021. Vol. 8. Is. 8. DOI: https://doi.org/10.1093/nsr/nwaa238
Sabia G., Mattioli D., Langone M., Petta L. Methodology for a preliminary assessment of water use sustainability in industries at sub-basin level. Journal of Environmental Management. 2023. Vol. 343. P. 118–163. DOI: https://doi.org/10.1016/j.jenvman.2023.118163
Toniolo S., Pieretto C., Camana D. Improving sustainability in communities: Linking the local scale to the concept of sustainable development. Environmental Impact Assessment Review. 2023. Vol. 101, P. 107–126. DOI: https://doi.org/10.1016/j.eiar.2023.107126
Correia E. Garrido-Azevedo S., Carvalho H. Supply Chain Sustainability: A Model to Assess the Maturity Level. Systems. 2023. № 11(2):98. DOI: https://doi.org/10.3390/systems11020098
Trishch R., Nechuiviter O., Dyadyura K., Vasilevskyi O., Tsykhanovska I., Yakovlev M. Qualimetric method of assessing risks of low quality products. MM Science Journal. 2021. P. 4769–4774. DOI: https://doi.org/10.17973/MMSJ.2021_10_2021030
Ginevičius R., Trišč R., Remeikienė R., Zielińska A., Strikaitė-Latušinskaja G. Evaluation of the condition of social processes based on qualimetric methods: The COVID-19 case. Journal of International Studies. 2022. №15(1). P. 230–249. DOI: https://doi.org/10.14254/2071-8330.2022/15-1/15
Trisch R., Gorbenko E., Dotsenko N., Kim N., Kiporenko G. Development of qualimetric approaches to the processes of quality management system at enterprises according to international standards of the ISO 9000 series. Eastern-European Journal of Enterprise Technologies. 2016. №4 (3-82). P. 18–24. DOI: https://doi.org/10.15587/1729-4061.2016.75503
Тріщ Р. М., Кіпоренко Г. С., Кім Н. І., Денисенко А. М. Оцінювання ризиків функціонування системи управління якістю (ДСТУ ISO 9001:2015) вищих навчальних заходів. Системи управління, навігації та зв'язку. Запобігання та ліквідація надзвичайних ситуацій. 2016. № 2(38). С. 133–136
Fisher R. A. On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society of London. Series A, Containing Papers of a Mathematical or Physical Character. 1922. № 222. P. 309–368
Neyman J. Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences. 1937. №236. P. 333–380. DOI: https://doi.org/10.1098/rsta.1937.0005
Anderson T. W, Stanley L. S. The Statistical Analysis of Data. Palo Alto, CA: Scientific Press. USA. 1986. 628 p.
Lehmann E. L., Joseph P. Testing Statistical Hypotheses. Springer Cham, 2022. DOI: https://doi.org/10.1007/978-3-030-70578-7
Jakobsson U., Westergren A. Statistical methods for assessing agreement for ordinal data. Scandinavian Journal of Caring Sciences. 2005. №19. P. 427–431. DOI: https://doi.org/10.1111/j.1471-6712.2005.00368.x
Moffat R. J. Using Uncertainty Analysis in the Planning of an Experiment. ASME. June 1985. № 107(2). P. 173–178. DOI: https://doi.org/10.1115/1.3242452
Robbins H. E. An Empirical Bayes Approach to Statistics. In: Kotz, S., Johnson, N.L. (eds) Breakthroughs in Statistics. Springer Series in Statistics. Springer: New York, 1992. DOI: https://doi.org/10.1007/978-1-4612-0919-5_26
Steiner S. H., MacKay R. J. Statistical engineering. Quality Press, 2005. 319 p.
Wald A. Sequential analysis. Courier Corporation, 2004. p. 212 p.
David H. Order statistics. John wiley and sons, 1970. 272 p.
Organisation for Economic Co-operation and Development (OECD). URL: https://www.oecd.org/ (дата звернення: 28.02.2024).
References
Liu, Y., Huang, B., Guo, H. (2023), "A big data approach to assess progress towards Sustainable Development Goals for cities of varying sizes", Commun Earth Environ, No. 4 (66). DOI: https://doi.org/10.1038/s43247-023-00730-8
Xu, Z., Chau, S.N., Chen, X. (2020), "Assessing progress towards sustainable development over space and time", Nature, No. 577, P. 74–78. DOI: https://doi.org/10.1038/s41586-019-1846-3
Yali Liu et al. (2021), "Evenness is important in assessing progress towards sustainable development goals", National Science Review, Volume 8, Issue 8. DOI: https://doi.org/10.1093/nsr/nwaa238
Sabia, G., Mattioli, D., Langone, M., Petta, L. (2023), "Methodology for a preliminary assessment of water use sustainability in industries at sub-basin level", Journal of Environmental Management, Vol. 343, P. 118–163, DOI: https://doi.org/10.1016/j.jenvman.2023.118163
Toniolo, S., Pieretto, C., Camana, D. (2023), "Improving sustainability in communities: Linking the local scale to the concept of sustainable development", Environmental Impact Assessment Review, Vol. 101, P. 107–126. DOI: https://doi.org/10.1016/j.eiar.2023.107126
Correia, E., Garrido-Azevedo, S., Carvalho, H. (2023), "Supply Chain Sustainability: A Model to Assess the Maturity Level", Systems, No. 11(2):98. DOI: https://doi.org/10.3390/systems11020098
Trishch, R., Nechuiviter, O., Dyadyura, K., Vasilevskyi, O., Tsykhanovska, I., Yakovlev, M. (2021), "Qualimetric method of assessing risks of low quality products", MM Science Journal, 2021-October, P. 4769–4774. DOI: https://doi.org/10.17973/MMSJ.2021_10_2021030
Ginevičius, R., Trišč, R., Remeikienė, R., Zielińska, A., Strikaitė-Latušinskaja, G. (2022), "Evaluation of the condition of social processes based on qualimetric methods: The COVID-19 case", Journal of International Studies, No. 15(1), P. 230–249. DOI: https://doi.org/10.14254/2071-8330.2022/15-1/15
Trisch, R., Gorbenko, E., Dotsenko, N., Kim, N., Kiporenko, H. (2016), "Development of qualimetric approaches to the processes of quality management system at enterprises according to international standards of the ISO 9000 series", Eastern-European Journal of Enterprise Technologies, No. 4 (3-82), P. 18–24. DOI: https://doi.org/10.15587/1729-4061.2016.75503
Trishch, R., Kiporenko, G., Kim, N., Denysenko, A. (2016), "Risk assessment of the quality management system (SSTС ISO 9001:2015) of higher education institutions" ["Otsiniuvannia ryzykiv funktsionuvannia systemy upravlinnia yakistiu (DSTU ISO 9001:2015) vyshchykh navchalnykh zakhodiv"]. Control, navigation and communication systems, No. 2 (38), P. 133–136.
Fisher, R. (1922), "On the mathematical foundations of theoretical statistics", Philosophical Transactions of the Royal Society of London, Series A, Containing Papers of a Mathematical or Physical Character, No. 222, P. 309–368.
Neyman, J. (1937), "Outline of a Theory of Statistical Estimation Based on the Classical Theory of Probability", Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, No. 236, P. 333–380. DOI: https://doi.org/10.1098/rsta.1937.0005
Anderson, T., Sclove, S. (1986), The Statistical Analysis of Data, Palo Alto, CA: Scientific Press, USA, 628 p.
Lehmann, E., Joseph, P. (2022), Testing Statistical Hypotheses, Springer Cham. DOI: https://doi.org/10.1007/978-3-030-70578-7
Jakobsson, U., Westergren, A. (2005), "Statistical methods for assessing agreement for ordinal data", Scandinavian Journal of Caring Sciences, No. 19, P. 427–431. DOI: https://doi.org/10.1111/j.1471-6712.2005.00368.x
Moffat, R. J. (June 1985), "Using Uncertainty Analysis in the Planning of an Experiment", ASME, No. 107(2), P. 173–178. DOI: https://doi.org/10.1115/1.3242452
Robbins, H. (1992), An Empirical Bayes Approach to Statistics, In: Kotz, S., Johnson, N. (eds) Breakthroughs in Statistics, Springer Series in Statistics, Springer, New York, NY. DOI: https://doi.org/10.1007/978-1-4612-0919-5_26
Steiner, S., MacKay, R. (2005), Statistical engineering, Quality Press. 319 p.
Wald, A. (2004), Sequential analysis, Courier Corporation. 212 p.
David, H. (1970), Order statistics, John wiley and sons, 272 p.
Organisation for Economic Co-operation and Development (OECD), available at: https://www.oecd.org/ (last accessed: 28.02.2024).
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