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DISCRIMINATING BETWEEN THE GAMMA AND WEIBULL DISTRIBUTIONS FOR GEOMETRIC PROCESS DATA

Year 2018, 18. EYI Special Issue, 239 - 252, 16.01.2018
https://doi.org/10.18092/ulikidince.353659

Abstract

To
obtain an optimal statistical analysis of the data observed in the
applications, the underlying distribution of the data set should be optimally
determined. Most of times, the goodness-of-fit tests used when trying to
determine the underlying distribution of a data set indicate more than one
distribution model to data set. Among the possible distribution models
according to the results of the goodness-of-fit tests, the problem of
determination of the optimal distribution model for the data set is quite
important problem in statistic. In this study, the problem of discriminating
between the Gamma and Weibull distributions for geometric process data is
investigated according to the ratio of maximum likelihood method. To show the
correct selection performance of the method used for discrimination, a
comprehensive simulation study is performed and in order to discriminating at
fixed level of confidence and power of test, required minimum sample sizes are
obtained. In addition, for illustrative purposes, an application is made by
using a real data set.

References

  • Ascher H. ve Feingold, H. (1984). Repairable systems reliability. New York: Marcel Dekker.
  • Aydoğdu, H., Şenoğlu, B. ve Kara, M. (2010). Parameter estimation in geometric process with We-ibull distribution. Applied Mathematics and Computation, 217(6), 2657-2665.
  • Bain, L. J. ve Engelhardt, M. (1980). Probability of correct selection of weibull versus gamma based on livelihood ratio. Communications in statistics-theory and methods, 9(4), 375-381.
  • Chan, J. S., Lam, Y. ve Leung, D. Y. (2004). Statistical inference for geometric processes with gamma distributions. Computational statistics & data analysis, 47(3), 565-581.
  • Dey, A. K. ve Kundu, D. (2012). Discriminating between the Weibull and log-normal distributions for Type-II censored data. Statistics, 46(2), 197-214.
  • Elsherpieny, E. A., Ibrahim, N. S. ve Radwan, N. U. (2013). Discriminating between Weibull and log-logistic distributions. International Journal of Innovative Research in Science, Engineering and Technology, 2(8), 3358-3371.
  • Fearn, D. H. ve Nebenzahl, E. (1991). On the maximum likelihood ratio method of deciding between the Weibull and Gamma distributions. Communications in Statistics-Theory and Methods, 20(2), 579-593.
  • Kara, M., Aydoğdu, H. ve Türkşen, Ö. (2015). Statistical inference for geometric process with the inverse Gaussian distribution. Journal of Statistical Computation and Simulation, 85(16), 3206-3215.
  • Kundu, D. ve Manglick, A. (2005). Discriminating between the log-normal and gamma distributions. Journal of the Applied Statistical Sciences, 14, 175-187.
  • Kundu, D. ve Manglick, A. (2004). Discriminating between the Weibull and log‐normal distributions Naval Research Logistics (NRL), 51(6), 893-905.
  • Kundu, D., Gupta, R. D., ve Manglick, A. (2005). Discriminating between the log-normal and genera-lized exponential distributions. Journal of Statistical Planning and Inference, 127(1), 213-227.
  • Kundu, D. ve Raqab, M. Z. (2007). Discriminating between the generalized Rayleigh and log-normal distribution. Statistics, 41(6), 505-515.
  • Lam, Y. (1988). Geometric processes and replacement problem. Acta Mathematicae Applicatae Sinica, 4, 366-377.
  • Lam, Y. (2007). The Geometric Process and Its Applications. Singapore: World Scientific.
  • Lam, Y. ve Chan, S. K. (1998). Statistical inference for geometric processes with lognormal distribu-tion. Computational statistics & data analysis, 27(1), 99-112.
  • Raqab, M. Z. (2013). Discriminating between the generalized Rayleigh and Weibull distributions. Journal of Applied Statistics, 40(7), 1480-1493.

GEOMETRİK SÜREÇ VERİLERİ İÇİN GAMMA VE WEİBULL DAĞILIMLARI ARASINDAKİ AYRIM

Year 2018, 18. EYI Special Issue, 239 - 252, 16.01.2018
https://doi.org/10.18092/ulikidince.353659

Abstract

Uygulamalarda gözlemlenen verilerin en uygun biçimde
istatistiksel analizini yapmak için veri kümesinin altında yatan dağılım en
uygun biçimde belirlenmelidir. Çoğu zaman, bir veri kümesinin altında yatan
dağılımı belirlemeye çalışırken kullanılan uyum iyiliği testleri, veri seti
için birden fazla dağılım modelini işaret eder. Uyum iyiliği testlerinin
sonuçlarına göre olası dağılım modelleri arasında, veri kümesi için optimal
dağılım modelinin belirlenmesi problemi, istatistikte oldukça önemli bir
problemdir. Bu çalışmada, geometric süreç verileri için Gamma ve Weibull
dağılımları arasındaki ayrım problemi, en çok olabilirlik oran yöntemine göre araştırılmıştır.
Ayrımcılık için kullanılan yöntemin doğru seçim performansını göstermek için,
kapsamlı bir simülasyon çalışması yapılmış ve belirli bir güven düzeyinde ve
test gücünde ayrım yapmak için gerekli minimum örneklem büyüklükleri elde
edilmiştir. Buna ek olarak, açıklayıcı amaçlarla, gerçek bir veri seti
kullanılarak bir uygulama yapılmıştır.

References

  • Ascher H. ve Feingold, H. (1984). Repairable systems reliability. New York: Marcel Dekker.
  • Aydoğdu, H., Şenoğlu, B. ve Kara, M. (2010). Parameter estimation in geometric process with We-ibull distribution. Applied Mathematics and Computation, 217(6), 2657-2665.
  • Bain, L. J. ve Engelhardt, M. (1980). Probability of correct selection of weibull versus gamma based on livelihood ratio. Communications in statistics-theory and methods, 9(4), 375-381.
  • Chan, J. S., Lam, Y. ve Leung, D. Y. (2004). Statistical inference for geometric processes with gamma distributions. Computational statistics & data analysis, 47(3), 565-581.
  • Dey, A. K. ve Kundu, D. (2012). Discriminating between the Weibull and log-normal distributions for Type-II censored data. Statistics, 46(2), 197-214.
  • Elsherpieny, E. A., Ibrahim, N. S. ve Radwan, N. U. (2013). Discriminating between Weibull and log-logistic distributions. International Journal of Innovative Research in Science, Engineering and Technology, 2(8), 3358-3371.
  • Fearn, D. H. ve Nebenzahl, E. (1991). On the maximum likelihood ratio method of deciding between the Weibull and Gamma distributions. Communications in Statistics-Theory and Methods, 20(2), 579-593.
  • Kara, M., Aydoğdu, H. ve Türkşen, Ö. (2015). Statistical inference for geometric process with the inverse Gaussian distribution. Journal of Statistical Computation and Simulation, 85(16), 3206-3215.
  • Kundu, D. ve Manglick, A. (2005). Discriminating between the log-normal and gamma distributions. Journal of the Applied Statistical Sciences, 14, 175-187.
  • Kundu, D. ve Manglick, A. (2004). Discriminating between the Weibull and log‐normal distributions Naval Research Logistics (NRL), 51(6), 893-905.
  • Kundu, D., Gupta, R. D., ve Manglick, A. (2005). Discriminating between the log-normal and genera-lized exponential distributions. Journal of Statistical Planning and Inference, 127(1), 213-227.
  • Kundu, D. ve Raqab, M. Z. (2007). Discriminating between the generalized Rayleigh and log-normal distribution. Statistics, 41(6), 505-515.
  • Lam, Y. (1988). Geometric processes and replacement problem. Acta Mathematicae Applicatae Sinica, 4, 366-377.
  • Lam, Y. (2007). The Geometric Process and Its Applications. Singapore: World Scientific.
  • Lam, Y. ve Chan, S. K. (1998). Statistical inference for geometric processes with lognormal distribu-tion. Computational statistics & data analysis, 27(1), 99-112.
  • Raqab, M. Z. (2013). Discriminating between the generalized Rayleigh and Weibull distributions. Journal of Applied Statistics, 40(7), 1480-1493.
There are 16 citations in total.

Details

Journal Section Articles
Authors

Cenker Biçer

Hayrinisa Demirci Biçer

Publication Date January 16, 2018
Published in Issue Year 2018 18. EYI Special Issue

Cite

APA Biçer, C., & Demirci Biçer, H. (2018). GEOMETRİK SÜREÇ VERİLERİ İÇİN GAMMA VE WEİBULL DAĞILIMLARI ARASINDAKİ AYRIM. Uluslararası İktisadi Ve İdari İncelemeler Dergisi239-252. https://doi.org/10.18092/ulikidince.353659

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