Araştırma Makalesi
BibTex RIS Kaynak Göster
Yıl 2017, Cilt: 18 Sayı: 2, 403 - 418, 30.06.2017
https://doi.org/10.18038/aubtda.289280

Öz

Kaynakça

  • Anand, S. and Sen, A. 1992. Human Development Index: Methodology and Measurement. Human Development Report Office Occasional Paper No. 12, UNDP, New York.
  • Azzalini, A. 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12(2), 171-178.
  • Azzalini, A. 1986. Further results on a class of distributions which includes the normal ones. Statistica, 46(2), 199-208.
  • Azzalini, A. and Capitanio, A. 2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 65(2), 367-389.
  • Basso, R. M., Lachos, V. H., Cabral, C. R. B. and Ghosh, P. 2010. Robust mixture modeling based on scale mixtures of skew-normal distributions. Computational Statistics & Data Analysis, 54(12), 2926-2941.
  • Bhanojirao, V.V. 1991. Human development report 1990: review and assessment. World Development, 19(10), 1451-1460.
  • Biernacki, C., Celeux, G. and Govaert, G. 2000. Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 719-725.
  • Bishop, C.M. 2006. Pattern Recognition and Machine Learning. Springer, Singapore.
  • Cabral, C.R.B., Lachos, V.H. and Prates, M.O. 2012. Multivariate mixture modeling using skew-normal independent distributions. Computational Statistics & Data Analysis, 56(1), 126-142.
  • Desai, M. 1991. Human development: Concept and measurement. European Economic Review 35, 350-357.
  • Dias, J.G. and Wedel, M. 2004. An empirical comparison of EM, SEM and MCMC performance for problematic gaussian mixture likelihoods. Statistics and Computing, 14, 323-332.
  • Doessel, D.P. and Gounder, R. 1991. International Comparisons of the Standards of Living and the Human Development Index. Discussion Papers in Economics No. 72, Department of Economics, University of Queensland, Brisbane.
  • Doğru, F.Z. and Arslan, O. 2017. Parameter estimation for mixtures of skew Laplace normal distributions and application in mixture regression modeling. Communications in Statistics: Theory and Methods, DOI: 10.1080/03610926.2016.1252400 (accepted).
  • Fraley, C. and Raftery, A.E. 1999. mclust: Software for model-based cluster analysis. Journal of Classification, 16, 297-306.
  • Fraley, C. and Raftery, A.E. 2002. Model-based clustering, discriminant analysis and density estimation. Journal of the American Statistical Association, 97, 611-631.
  • Fraley, C. and Raftery, A.E. 2003. Enhanced software for model-based clustering, density estimation, and discriminant analysis: mclust. Journal of Classification, 20, 263-286.
  • Fraley, C. and Raftery, A.E. 2006. Model-based Microarray Image Analysis. R News, 6, 60-63.
  • Frühwirth-Schnatter, S. 2006. Finite Mixture and Markov Switching Models. Springer, New York.
  • Ho, H., Pyne, S. and Lin, T. 2012. Maximum likelihood inference for mixtures of skew Student-t-normal distributions through practical EM-type algorithms. Statistics and Computing, 22(1), 287-299.
  • Hopkins, M. (1991). Human development revisited: A new UNDP report. World Development, 19(10), 1469-1473.
  • Kaufman, L. and P.J. Rousseeuw. 1990. Finding Groups in Data: An Introduction to Cluster Analysis, New York: John Wiley & Sons.
  • Kelley, A.C. 1991. The Human Development Index:" Handle with Care". Population and Development Review, 315-324.
  • Lin, T.I., Lee, J.C. and Hsieh, W.J. 2007a. Robust mixture modeling using the skew t distribution. Statistics and Computing, 17, 81–92.
  • Lin, T.I., Lee, J.C. and Yen, S.Y. 2007b. Finite mixture modelling using the skew normal distribution. Statistica Sinica, 17(3), 909–927.
  • Lind, N. C. 1992. Some thoughts on the human development index. Social Indicators Research, 27(1), 89-101.
  • McGillivray, M. 1991. The human development index: yet another redundant composite development indicator?. World Development, 19(10), 1461-1468.
  • McGillivray, M. and White, H. 1992. Measuring development?: a statistical critique of the UNDP's human development index. ISS Working Paper Series/General Series, 135, 1-25.
  • McLachlan, G.J. 1987. On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Journal of the Royal Statistical Society C, 36, 318-324.
  • McLachlan, G.J. and Basford, K.E. 1988. Mixture Models: Inference and Application to Clustering. Marcel Dekker, New York.
  • McLachlan, G.J. and Peel, D. 2000. Finite Mixture Models. Wiley, New York.
  • Peel D. and McLachlan G.J. 2000. Robust mixture modeling using the t distribution. Statistics and Computing, 10, 339-348.
  • Prates, M.O., Lachos, V.H. and Cabral, C. 2011. mixsmsn: Fitting finite mixture of scale mixture of skew-normal distributions. R package version 0.3-2.
  • Prates, M.O., Lachos, V.H. and Cabral, C. 2013. mixsmsn: Fitting finite mixture of scale mixture of skew-normal distributions. Journal of Statistical Software, 54(12), 1-20.
  • Pyatt, G. 1991. Poverty: a wasted decade. European economic review, 35(2-3), 358-365.
  • Titterington, D.M., Smith, A.F.M. and Markov, U.E. 1985. Statistical Analysis of Finite Mixture Distributions. Wiley, New York.
  • Trabold-Nübler, H. 1991. The human development index-a new development indicator?. Intereconomics, 26(5), 236-243.
  • UNDP. 1990. Human Development Report 1990. Oxford University Press, New York.
  • UNDP. 2015. Human Development Report 2015. Oxford University Press, New York.

Modeling Human Development Index Using Finite Mixtures of Distributions

Yıl 2017, Cilt: 18 Sayı: 2, 403 - 418, 30.06.2017
https://doi.org/10.18038/aubtda.289280

Öz

The Human Development Index
(HDI) measures development of a country which was designed by the United
Nations Development Programme (UNDP). Since the values of HDI for different
countries show differences according to the development of a country, the distribution
of HDI may have one more mode, thick tail or skewness. Therefore, we can use
mixtures of distributions to model the HDI data set to handle modality,
heavy-tailedness and/or skewness. In this paper, we propose finite mixtures of distributions
to model the data from the HDI report 2015 for 186 countries. We give the basic
scheme of the maximum likelihood (ML) estimation using Expectation-Maximization
(EM) algorithm for finite mixture model. To obtain best model for HDI data set,
we first find the appropriate cluster number using model-based clustering.
Then, we use the finite mixture models obtained from some symmetric and/or
heavy-tailed and skew and/or heavy-tailed distributions to find the best model for HDI data set.

Kaynakça

  • Anand, S. and Sen, A. 1992. Human Development Index: Methodology and Measurement. Human Development Report Office Occasional Paper No. 12, UNDP, New York.
  • Azzalini, A. 1985. A class of distributions which includes the normal ones. Scandinavian Journal of Statistics, 12(2), 171-178.
  • Azzalini, A. 1986. Further results on a class of distributions which includes the normal ones. Statistica, 46(2), 199-208.
  • Azzalini, A. and Capitanio, A. 2003. Distributions generated by perturbation of symmetry with emphasis on a multivariate skew t distribution. Journal of the Royal Statistical Society, Series B (Statistical Methodology), 65(2), 367-389.
  • Basso, R. M., Lachos, V. H., Cabral, C. R. B. and Ghosh, P. 2010. Robust mixture modeling based on scale mixtures of skew-normal distributions. Computational Statistics & Data Analysis, 54(12), 2926-2941.
  • Bhanojirao, V.V. 1991. Human development report 1990: review and assessment. World Development, 19(10), 1451-1460.
  • Biernacki, C., Celeux, G. and Govaert, G. 2000. Assessing a mixture model for clustering with the integrated completed likelihood. IEEE Transactions on Pattern Analysis and Machine Intelligence, 22, 719-725.
  • Bishop, C.M. 2006. Pattern Recognition and Machine Learning. Springer, Singapore.
  • Cabral, C.R.B., Lachos, V.H. and Prates, M.O. 2012. Multivariate mixture modeling using skew-normal independent distributions. Computational Statistics & Data Analysis, 56(1), 126-142.
  • Desai, M. 1991. Human development: Concept and measurement. European Economic Review 35, 350-357.
  • Dias, J.G. and Wedel, M. 2004. An empirical comparison of EM, SEM and MCMC performance for problematic gaussian mixture likelihoods. Statistics and Computing, 14, 323-332.
  • Doessel, D.P. and Gounder, R. 1991. International Comparisons of the Standards of Living and the Human Development Index. Discussion Papers in Economics No. 72, Department of Economics, University of Queensland, Brisbane.
  • Doğru, F.Z. and Arslan, O. 2017. Parameter estimation for mixtures of skew Laplace normal distributions and application in mixture regression modeling. Communications in Statistics: Theory and Methods, DOI: 10.1080/03610926.2016.1252400 (accepted).
  • Fraley, C. and Raftery, A.E. 1999. mclust: Software for model-based cluster analysis. Journal of Classification, 16, 297-306.
  • Fraley, C. and Raftery, A.E. 2002. Model-based clustering, discriminant analysis and density estimation. Journal of the American Statistical Association, 97, 611-631.
  • Fraley, C. and Raftery, A.E. 2003. Enhanced software for model-based clustering, density estimation, and discriminant analysis: mclust. Journal of Classification, 20, 263-286.
  • Fraley, C. and Raftery, A.E. 2006. Model-based Microarray Image Analysis. R News, 6, 60-63.
  • Frühwirth-Schnatter, S. 2006. Finite Mixture and Markov Switching Models. Springer, New York.
  • Ho, H., Pyne, S. and Lin, T. 2012. Maximum likelihood inference for mixtures of skew Student-t-normal distributions through practical EM-type algorithms. Statistics and Computing, 22(1), 287-299.
  • Hopkins, M. (1991). Human development revisited: A new UNDP report. World Development, 19(10), 1469-1473.
  • Kaufman, L. and P.J. Rousseeuw. 1990. Finding Groups in Data: An Introduction to Cluster Analysis, New York: John Wiley & Sons.
  • Kelley, A.C. 1991. The Human Development Index:" Handle with Care". Population and Development Review, 315-324.
  • Lin, T.I., Lee, J.C. and Hsieh, W.J. 2007a. Robust mixture modeling using the skew t distribution. Statistics and Computing, 17, 81–92.
  • Lin, T.I., Lee, J.C. and Yen, S.Y. 2007b. Finite mixture modelling using the skew normal distribution. Statistica Sinica, 17(3), 909–927.
  • Lind, N. C. 1992. Some thoughts on the human development index. Social Indicators Research, 27(1), 89-101.
  • McGillivray, M. 1991. The human development index: yet another redundant composite development indicator?. World Development, 19(10), 1461-1468.
  • McGillivray, M. and White, H. 1992. Measuring development?: a statistical critique of the UNDP's human development index. ISS Working Paper Series/General Series, 135, 1-25.
  • McLachlan, G.J. 1987. On bootstrapping the likelihood ratio test statistic for the number of components in a normal mixture. Journal of the Royal Statistical Society C, 36, 318-324.
  • McLachlan, G.J. and Basford, K.E. 1988. Mixture Models: Inference and Application to Clustering. Marcel Dekker, New York.
  • McLachlan, G.J. and Peel, D. 2000. Finite Mixture Models. Wiley, New York.
  • Peel D. and McLachlan G.J. 2000. Robust mixture modeling using the t distribution. Statistics and Computing, 10, 339-348.
  • Prates, M.O., Lachos, V.H. and Cabral, C. 2011. mixsmsn: Fitting finite mixture of scale mixture of skew-normal distributions. R package version 0.3-2.
  • Prates, M.O., Lachos, V.H. and Cabral, C. 2013. mixsmsn: Fitting finite mixture of scale mixture of skew-normal distributions. Journal of Statistical Software, 54(12), 1-20.
  • Pyatt, G. 1991. Poverty: a wasted decade. European economic review, 35(2-3), 358-365.
  • Titterington, D.M., Smith, A.F.M. and Markov, U.E. 1985. Statistical Analysis of Finite Mixture Distributions. Wiley, New York.
  • Trabold-Nübler, H. 1991. The human development index-a new development indicator?. Intereconomics, 26(5), 236-243.
  • UNDP. 1990. Human Development Report 1990. Oxford University Press, New York.
  • UNDP. 2015. Human Development Report 2015. Oxford University Press, New York.
Toplam 38 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Araştırma Makalesi
Yazarlar

Fatma Zehra Doğru 0000-0001-8220-2375

Yayımlanma Tarihi 30 Haziran 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 18 Sayı: 2

Kaynak Göster

APA Doğru, F. Z. (2017). Modeling Human Development Index Using Finite Mixtures of Distributions. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, 18(2), 403-418. https://doi.org/10.18038/aubtda.289280
AMA Doğru FZ. Modeling Human Development Index Using Finite Mixtures of Distributions. AUBTD-A. Haziran 2017;18(2):403-418. doi:10.18038/aubtda.289280
Chicago Doğru, Fatma Zehra. “Modeling Human Development Index Using Finite Mixtures of Distributions”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 18, sy. 2 (Haziran 2017): 403-18. https://doi.org/10.18038/aubtda.289280.
EndNote Doğru FZ (01 Haziran 2017) Modeling Human Development Index Using Finite Mixtures of Distributions. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 18 2 403–418.
IEEE F. Z. Doğru, “Modeling Human Development Index Using Finite Mixtures of Distributions”, AUBTD-A, c. 18, sy. 2, ss. 403–418, 2017, doi: 10.18038/aubtda.289280.
ISNAD Doğru, Fatma Zehra. “Modeling Human Development Index Using Finite Mixtures of Distributions”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering 18/2 (Haziran 2017), 403-418. https://doi.org/10.18038/aubtda.289280.
JAMA Doğru FZ. Modeling Human Development Index Using Finite Mixtures of Distributions. AUBTD-A. 2017;18:403–418.
MLA Doğru, Fatma Zehra. “Modeling Human Development Index Using Finite Mixtures of Distributions”. Anadolu University Journal of Science and Technology A - Applied Sciences and Engineering, c. 18, sy. 2, 2017, ss. 403-18, doi:10.18038/aubtda.289280.
Vancouver Doğru FZ. Modeling Human Development Index Using Finite Mixtures of Distributions. AUBTD-A. 2017;18(2):403-18.

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