BibTex RIS Kaynak Göster

COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY

Yıl 2014, Cilt: 7 Sayı: 2, 33 - 42, 01.06.2014

Öz

Heterogeneous survival data can have two different distributions before and after a certain timebecause many factors affect the life of the creatures or machines. For this purpose, we use a mixture of twoidentical (same kind of) distributions of Exponential, Gamma, Lognormal and Weibull and also all pairwisecombinations of these distributions. In addition to the previous studies, we propose the mixture of Log-normaldistribution with the Exponential, Gamma and Weibull distributions. Maximum likelihood estimations ofparameters of the mixture distribution models are obtained by using the EM (Expectation Maximization)algorithm. Model performances are compared using goodness of fit tests and Akaike’s information criterion(AIC). Results indicate that, mixtures of two non-identical (different kind of) distributions are as useful asmixtures of identical distributions

Kaynakça

  • Berkson, J. and Gage, RP. (1952). Survival curve for cancer patients following treatment. Journal of the American Statistical Association, 47(259), 501-515. [2] Chen, WC., Hill, B., Greenhouse, J. and Fayos, J. (1985). Bayesian analysis of survival curves for cancer patients following treatment. Bayesian statistics, 2, 299-328.
  • Dempster, AP., Laird, NM. and Rubin, DB. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society, Series B (Methodological), 1-38.
  • Dirican, A. (2004). The patients with lung cancer were diagnosed in our clinic as a prospective evaluation and determination of the factors that affect survival. Master’s thesis, Ondokuz Mayis University.
  • Ebeling, CE. (1997). An introduction to reliability and maintainability engineering. The Mcgraw-Hill Companies, Inc., New York.
  • Elandt-Johnson, RC. and Johnson, NL. (1980). Survival models and data analysis. John Wiley & Sons. [7] Eri¸so˘glu, M., C¸ alı¸s, N., Servi, T., Eri¸so˘glu, ¨U. and Topaksu, M. (2011a). The mixture distribution models for interoccurence times of earthquakes. Russian Geology and Geophysics, 52, 685-692.
  • Eri¸so˘glu, ¨U., Eri¸so˘glu, M. and Erol, H. (2011b.) A mixture model of two different distributions approach to the analysis of heterogeneous survival data. International Journal of Computational and Mathematical Sciences, 5(2) ,75-79.
  • Eri¸so˘glu, ¨U., Eri¸so˘glu, M. and Erol, H. (2012). Mixture model approach to the analysis of heterogeneous survival data. Pakistan Journal of Statistics, 28(1), 115-130.
  • Everitt, BS. and Hand, DJ. (1981). Finite mixture distributions. London: Chapman and Hall.
  • Jiang, R. and Murthy, D. (1995). Modeling failure-data by mixture of 2 weibull distributions: a graphical approach. Reliability, IEEE Transactions on, 44(3), 477-488.
  • Jiang, R.and Murthy, D. (1997). Two sectional models involving three weibull distributions. Quality and Reliability Engineering International, 13(2), 83-96. [13] Lawless, JF. (2011). Statistical models and methods for lifetime data. John Wiley & Sons.
  • Lee, ET. and Wang, J. (2003). Statistical methods for survival data analysis. John Wiley & Sons.
  • Marin, J., Rodriguez-Bernal, M. and Wiper, M. (2005). Using weibull mixture distributions to model heterogeneous survival data. Communications in Statistics-Simulation and Computation, 34(3), 673-684. [16] McLachlan, G. and Peel, D. (2004). Finite mixture models. John Wiley & Sons.
  • Qian, J. (1994). A bayesian weibull survival model. PhD thesis, Institute of Statistical and Decision Sciences Duke University: North Corolina.
  • Zhang, Y. (2008). Parametric mixture models in survival analysis with applications. PhD thesis, Temple University.
Yıl 2014, Cilt: 7 Sayı: 2, 33 - 42, 01.06.2014

Öz

Kaynakça

  • Berkson, J. and Gage, RP. (1952). Survival curve for cancer patients following treatment. Journal of the American Statistical Association, 47(259), 501-515. [2] Chen, WC., Hill, B., Greenhouse, J. and Fayos, J. (1985). Bayesian analysis of survival curves for cancer patients following treatment. Bayesian statistics, 2, 299-328.
  • Dempster, AP., Laird, NM. and Rubin, DB. (1977). Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society, Series B (Methodological), 1-38.
  • Dirican, A. (2004). The patients with lung cancer were diagnosed in our clinic as a prospective evaluation and determination of the factors that affect survival. Master’s thesis, Ondokuz Mayis University.
  • Ebeling, CE. (1997). An introduction to reliability and maintainability engineering. The Mcgraw-Hill Companies, Inc., New York.
  • Elandt-Johnson, RC. and Johnson, NL. (1980). Survival models and data analysis. John Wiley & Sons. [7] Eri¸so˘glu, M., C¸ alı¸s, N., Servi, T., Eri¸so˘glu, ¨U. and Topaksu, M. (2011a). The mixture distribution models for interoccurence times of earthquakes. Russian Geology and Geophysics, 52, 685-692.
  • Eri¸so˘glu, ¨U., Eri¸so˘glu, M. and Erol, H. (2011b.) A mixture model of two different distributions approach to the analysis of heterogeneous survival data. International Journal of Computational and Mathematical Sciences, 5(2) ,75-79.
  • Eri¸so˘glu, ¨U., Eri¸so˘glu, M. and Erol, H. (2012). Mixture model approach to the analysis of heterogeneous survival data. Pakistan Journal of Statistics, 28(1), 115-130.
  • Everitt, BS. and Hand, DJ. (1981). Finite mixture distributions. London: Chapman and Hall.
  • Jiang, R. and Murthy, D. (1995). Modeling failure-data by mixture of 2 weibull distributions: a graphical approach. Reliability, IEEE Transactions on, 44(3), 477-488.
  • Jiang, R.and Murthy, D. (1997). Two sectional models involving three weibull distributions. Quality and Reliability Engineering International, 13(2), 83-96. [13] Lawless, JF. (2011). Statistical models and methods for lifetime data. John Wiley & Sons.
  • Lee, ET. and Wang, J. (2003). Statistical methods for survival data analysis. John Wiley & Sons.
  • Marin, J., Rodriguez-Bernal, M. and Wiper, M. (2005). Using weibull mixture distributions to model heterogeneous survival data. Communications in Statistics-Simulation and Computation, 34(3), 673-684. [16] McLachlan, G. and Peel, D. (2004). Finite mixture models. John Wiley & Sons.
  • Qian, J. (1994). A bayesian weibull survival model. PhD thesis, Institute of Statistical and Decision Sciences Duke University: North Corolina.
  • Zhang, Y. (2008). Parametric mixture models in survival analysis with applications. PhD thesis, Temple University.
Toplam 14 adet kaynakça vardır.

Ayrıntılar

Diğer ID JA75ER57HZ
Bölüm Araştırma Makalesi
Yazarlar

Ayça Hatice Türkan Bu kişi benim

Nazif Çalış. Bu kişi benim

Yayımlanma Tarihi 1 Haziran 2014
Yayımlandığı Sayı Yıl 2014 Cilt: 7 Sayı: 2

Kaynak Göster

APA Türkan, A. H., & Çalış., N. (2014). COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY. Istatistik Journal of The Turkish Statistical Association, 7(2), 33-42.
AMA Türkan AH, Çalış. N. COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY. IJTSA. Haziran 2014;7(2):33-42.
Chicago Türkan, Ayça Hatice, ve Nazif Çalış. “COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY”. Istatistik Journal of The Turkish Statistical Association 7, sy. 2 (Haziran 2014): 33-42.
EndNote Türkan AH, Çalış. N (01 Haziran 2014) COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY. Istatistik Journal of The Turkish Statistical Association 7 2 33–42.
IEEE A. H. Türkan ve N. Çalış., “COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY”, IJTSA, c. 7, sy. 2, ss. 33–42, 2014.
ISNAD Türkan, Ayça Hatice - Çalış., Nazif. “COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY”. Istatistik Journal of The Turkish Statistical Association 7/2 (Haziran 2014), 33-42.
JAMA Türkan AH, Çalış. N. COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY. IJTSA. 2014;7:33–42.
MLA Türkan, Ayça Hatice ve Nazif Çalış. “COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY”. Istatistik Journal of The Turkish Statistical Association, c. 7, sy. 2, 2014, ss. 33-42.
Vancouver Türkan AH, Çalış. N. COMPARISON OF TWO-COMPONENT MIXTURE DISTRIBUTION MODELS FOR HETEROGENEOUS SURVIVAL DATASETS: A REVIEW STUDY. IJTSA. 2014;7(2):33-42.