Pub Date : 2015-09-30DOI: 10.5604/01.3001.0014.1755
Marcin Pełka, A. Dudek
Interval-valued data can find their practical applications in such situations as recording monthly interval temperatures at meteorological stations, daily interval stock prices, etc. The primary objective of the presented paper is to compare three different methods of fuzzy clustering for interval-valued symbolic data, i.e.: fuzzy c-means clustering, adaptive fuzzy c-means clustering and fuzzy k-means clustering with fuzzy spectral clustering. Fuzzy spectral clustering combines both spectral and fuzzy approaches in order to obtain better results (in terms of Rand index for fuzzy clustering). The conducted simulation studies with artificial and real data sets confirm both higher usefulness and more stable results of fuzzy spectral clustering method, as compared to other existing fuzzy clustering methods for symbolic interval-valued data, when dealing with data featuring different cluster structures, noisy variables and/or outliers.
{"title":"The Comparison of Fuzzy Clustering Methods for Symbolic Interval-Valued Data","authors":"Marcin Pełka, A. Dudek","doi":"10.5604/01.3001.0014.1755","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1755","url":null,"abstract":"Interval-valued data can find their practical applications in such situations as recording monthly interval temperatures at meteorological stations, daily interval stock prices, etc. The primary objective of the presented paper is to compare three different methods of fuzzy clustering for interval-valued symbolic data, i.e.: fuzzy c-means clustering, adaptive fuzzy c-means clustering and fuzzy k-means clustering with fuzzy spectral clustering. Fuzzy spectral clustering combines both spectral and fuzzy approaches in order to obtain better results (in terms of Rand index for fuzzy clustering). The conducted simulation studies with artificial and real data sets confirm both higher usefulness and more stable results of fuzzy spectral clustering method, as compared to other existing fuzzy clustering methods for symbolic interval-valued data, when dealing with data featuring different cluster structures, noisy variables and/or outliers.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126328809","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-30DOI: 10.5604/01.3001.0014.1754
A. Lipieta
The trajectories illustrating the necessary changes in the production sphere, which are caused by the necessity or the wish of producers, who adjust their activities to the given requirements, are analyzed in the paper. The producers’ activities are modeled in the Debreu economy, while the requirements are given analytically, by using the linear functionals. If the producers change their plans of action due to the considered trajectories, equilibrium in the economy will be kept, although the initial state of equilibrium can be replaced by the other one. In the set of trajectories under study, the preference relation is defined. Under some assumptions, the maximal element of the above relation, so called the best producers’ adjustment trajectory, indicates the best path of changes in producers’ activities, under the criterion of losses minimization.
{"title":"The Optimal Producers’ Adjustment Trajectory","authors":"A. Lipieta","doi":"10.5604/01.3001.0014.1754","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1754","url":null,"abstract":"The trajectories illustrating the necessary changes in the production sphere, which are caused by the necessity or the wish of producers, who adjust their activities to the given requirements, are analyzed in the paper. The producers’ activities are modeled in the Debreu economy, while the requirements are given analytically, by using the linear functionals.\u0000If the producers change their plans of action due to the considered trajectories, equilibrium in the economy will be kept, although the initial state of equilibrium can be replaced by the other one.\u0000In the set of trajectories under study, the preference relation is defined. Under some assumptions, the maximal element of the above relation, so called the best producers’ adjustment trajectory, indicates the best path of changes in producers’ activities, under the criterion of losses minimization.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117217544","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-09-30DOI: 10.5604/01.3001.0014.1753
S. Kot
The paper presents the concept of the stochastic equivalence scale (SES), which is based on the stochastic indifference criterion. The SES is any function that transforms the expenditure distribution of a specific group of households in such a way that the resulting distribution is stochastically indifferent from the expenditure distribution of a reference group of households. The stochastic indifference criteria are also used in developing the method of the estimation of the SES. Non-parametric and parametric SESs are estimated using the Polish Household Budget Survey for the years 2005–2010.
{"title":"Equivalence Scales Based on Stochastic Indifference Criterion: The Case of Poland","authors":"S. Kot","doi":"10.5604/01.3001.0014.1753","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1753","url":null,"abstract":"The paper presents the concept of the stochastic equivalence scale (SES), which is based on the stochastic indifference criterion. The SES is any function that transforms the expenditure distribution of a specific group of households in such a way that the resulting distribution is stochastically indifferent from the expenditure distribution of a reference group of households. The stochastic indifference criteria are also used in developing the method of the estimation of the SES. Non-parametric and parametric SESs are estimated using the Polish Household Budget Survey for the years 2005–2010.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"7 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128334917","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-30DOI: 10.5604/01.3001.0014.1748
K. Kukuła, L. Luty
In this paper there was analyzed the issue of the selection of linear ordering method based on synthetic variable. The research of the status of waste management in Polish voivodeships in 2012 showed that selection procedures for the construction of synthetic variable affects the ranking of the objects under investigation. In the paper authors proposed a method supporting decision to select linear ordering procedure based on between ranking linear comparison measure (Kukuła, 1989). The choice of ordering methods with the use of the proposed procedure, of course, depends largely on the output of the set of ordering procedures. The test results indicate that there is no universal method.
{"title":"The Proposal for the Procedure Supporting Selection of a Linear Ordering Method","authors":"K. Kukuła, L. Luty","doi":"10.5604/01.3001.0014.1748","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1748","url":null,"abstract":"In this paper there was analyzed the issue of the selection of linear ordering method based on synthetic variable. The research of the status of waste management in Polish voivodeships in 2012 showed that selection procedures for the construction of synthetic variable affects the ranking of the objects under investigation. In the paper authors proposed a method supporting decision to select linear ordering procedure based on between ranking linear comparison measure (Kukuła, 1989). The choice of ordering methods with the use of the proposed procedure, of course, depends largely on the output of the set of ordering procedures. The test results indicate that there is no universal method.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"55 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127934331","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-30DOI: 10.5604/01.3001.0014.1741
D. Siudak
The article looks at the community structure in the network of interlocking directorates. The study covered 518 enterprises within the largest component of the total of 902 companies listed on the main market at the Warsaw Stock Exchange and on the NewConnect at the end of 2014. The strength of the community structure was assessed using the distribution function for quality (modularity), calculated for seven divisions of enterprises with different algorithms, respectively. The analysis led to the conclusion that the community structure existing in the board network between enterprises on Polish capital market is strong.
{"title":"Community Structure in the Boards Network of Enterprises on Polish Capital Market","authors":"D. Siudak","doi":"10.5604/01.3001.0014.1741","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1741","url":null,"abstract":"The article looks at the community structure in the network of interlocking directorates. The study covered 518 enterprises within the largest component of the total of 902 companies listed on the main market at the Warsaw Stock Exchange and on the NewConnect at the end of 2014. The strength of the community structure was assessed using the distribution function for quality (modularity), calculated for seven divisions of enterprises with different algorithms, respectively. The analysis led to the conclusion that the community structure existing in the board network between enterprises on Polish capital market is strong.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"187 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124737974","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-30DOI: 10.5604/01.3001.0014.1759
E. Panek
In the reference to articles Panek (2014, 2015) in the paper two version of the so called twisted turnpike in the nonstationary Gale economy are presented. There states that if in the non-stationary Gale economy the optimal growth process in the certain period of the time reaches the twisted turnpike and the von Neumann prices do not change to abruptly, than irrespectively of the length of the horizon of the economy such a process for all next periods can be found in the turnpike’s proximity, except for perhaps the final time.
{"title":"Twisted Turnpike in the Non-Stationary Gale Economy. Part II","authors":"E. Panek","doi":"10.5604/01.3001.0014.1759","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1759","url":null,"abstract":"In the reference to articles Panek (2014, 2015) in the paper two version of the so called twisted turnpike in the nonstationary Gale economy are presented. There states that if in the non-stationary Gale economy the optimal growth process in the certain period of the time reaches the twisted turnpike and the von Neumann prices do not change to abruptly, than irrespectively of the length of the horizon of the economy such a process for all next periods can be found in the turnpike’s proximity, except for perhaps the final time.","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127765876","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-30DOI: 10.5604/01.3001.0014.1750
E. Panek
The article contains a correction of lemma 1 proof and the consequently “strong” turnpike theorem 3 as presented in the work by Panek (2013).
本文包含对引理1证明的更正，以及Panek(2013)在工作中提出的“强”收费公路定理3。
{"title":"“Strong” Turnpike Effect in the Gale Economic Dynamics Model. Finite State Growth Problem (Self-Correction)","authors":"E. Panek","doi":"10.5604/01.3001.0014.1750","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1750","url":null,"abstract":"The article contains a correction of lemma 1 proof and the consequently “strong” turnpike theorem 3 as presented in the work by Panek (2013).\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130191467","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-30DOI: 10.5604/01.3001.0014.1739
D. Kacprzak
In the paper, a new approach to fuzzy Multi-Attribute Decision Making methods has been proposed, with the application of Ordered Fuzzy Numbers model. After the presentation of OFN model, it has been used as part of the fuzzy SAW method. Ordered fuzzy numbers allow to immediately distinguish between type of criteria, and the presented examples show the usefulness of the proposed method.
{"title":"FSAW Method Using Ordered Fuzzy Numbers","authors":"D. Kacprzak","doi":"10.5604/01.3001.0014.1739","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1739","url":null,"abstract":"In the paper, a new approach to fuzzy Multi-Attribute Decision Making methods has been proposed, with the application of Ordered Fuzzy Numbers model. After the presentation of OFN model, it has been used as part of the fuzzy SAW method. Ordered fuzzy numbers allow to immediately distinguish between type of criteria, and the presented examples show the usefulness of the proposed method.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"70 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130098765","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-30DOI: 10.5604/01.3001.0014.1742
Marcin Topolewski
The work concerns the applicability of credibility estimators of order higher than one, called hierarchical estimators, to posterior estimates of claim ratio in motor insurance systems based on the history of the insured. The first part presents the idea of the credibility estimation method. In the second part the linear credibility estimator is discussed. The third part introduces appropriate for risk models in the form of claims distributions, which are used to derive the corresponding hierarchical estimates of the first order. The fourth section expands the discussion of the hierarchical estimators of the order two. In the empirical fifth part previously presented solutions are used to estimate the loss ratio for the sample insurance portfolio, results are discussed and conclusions concerning the possibility of application of second order hierarchical estimators into motor insurance are formulated.
{"title":"Analysis of Possibility of Application of Higher-Order Hierarchical Credibility Estimators in Automobile Insurance","authors":"Marcin Topolewski","doi":"10.5604/01.3001.0014.1742","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1742","url":null,"abstract":"The work concerns the applicability of credibility estimators of order higher than one, called hierarchical estimators, to posterior estimates of claim ratio in motor insurance systems based on the history of the insured. The first part presents the idea of the credibility estimation method. In the second part the linear credibility estimator is discussed. The third part introduces appropriate for risk models in the form of claims distributions, which are used to derive the corresponding hierarchical estimates of the first order. The fourth section expands the discussion of the hierarchical estimators of the order two. In the empirical fifth part previously presented solutions are used to estimate the loss ratio for the sample insurance portfolio, results are discussed and conclusions concerning the possibility of application of second order hierarchical estimators into motor insurance are formulated.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127346586","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2015-06-30DOI: 10.5604/01.3001.0014.1749
M. Steć
The paper contains the statistical analysis of EU countries in terms of the implementation of the Europe 2020 Strategy. Basis for evaluation are the main indicators proposed by Eurostat to monitor the progress of the EU countries in implementing this concept development. The method used in this work is the Z. Hellwig and zeroed unitarisation method. The study covered the period 2009–2013. The study shows that EU countries have different levels of implementation of the Europe 2020 Strategy, which is reflected in their classification into groups with different levels.
{"title":"Statistical Analysis of Europe 2020 Strategy Implementation in the European Union Countries","authors":"M. Steć","doi":"10.5604/01.3001.0014.1749","DOIUrl":"https://doi.org/10.5604/01.3001.0014.1749","url":null,"abstract":"The paper contains the statistical analysis of EU countries in terms of the implementation of the Europe 2020 Strategy. Basis for evaluation are the main indicators proposed by Eurostat to monitor the progress of the EU countries in implementing this concept development. The method used in this work is the Z. Hellwig and zeroed unitarisation method. The study covered the period 2009–2013. The study shows that EU countries have different levels of implementation of the Europe 2020 Strategy, which is reflected in their classification into groups with different levels.\u0000\u0000","PeriodicalId":357447,"journal":{"name":"Przegląd Statystyczny","volume":"57 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-06-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127184347","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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