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Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample

Year 2021, Volume: 25 Issue: 1, 49 - 53, 20.04.2021

Mehtap Koca Yunus Akdoğan Kadir Karakaya

https://doi.org/10.19113/sdufenbed.699703

Abstract

Recently, many new discrete distributions have been obtained. The uniform-geometric distribution is a newly obtained discrete distribution. In literature, parameter estimation is rare in the case of censored samples for new discrete distributions. In this study, the parameter estimation based on type-I censored sampling for the unknown parameter of the uniform geometric distribution is obtained using the maximum likelihood, methods of proportions, methods of moments, and modified maximum likelihood estimation methods. The performance of estimation methods is compared using the Monte Carlo simulation via biases and mean squared errors. Finally, two real data applications are given.

Keywords

Uniform-Geometric distribution Maximum likelihood Modified maximum likelihood Method of moments Method of proportions

References

  • [1] Lawless, J. F. 1982. Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York, 580p.
  • [2] Sinha, S. K. 1986. Reliability and Life testing. Wiley Eastern Ltd, New Delhi, 252p.
  • [3] Nakagawa, T., Osaki, S. 1975. This discrete Weibull distribution. IEEE Transactions on Reliability, 24, 300-301.
  • [4] Stein, W. E., Dattero, R. 1984. A new discrete Weibull distribution. IEEE Transactions on Reliability, 33, 196-197.
  • [5] Roy, D. 2003. The discrete normal distribution. Communications in Statistics Theory and Methods, 32, 1871-1883.
  • [6] Roy, D. 2004. Discrete Rayleigh distribution. IEEE Transactions on Reliability, 53(2), 255-260.
  • [7] Krishna, H., Pundir, P. S. 2009. Discrete Burr and discrete Pareto Distributions. Statistical Methodology, 6, 177-188.
  • [8] Jazi, M. A, Lai, C. D., Alamatsaz, M.H. 2009. A discrete inverse Weibull distribution and estimation of its parameters. Statistical Methodology, 7, 121-132.
  • [9] Hu, Y., Peng, X., Li, T., Guo, H. 2017. On the Poisson approximation to photon distribution for faint lasers. Phys Lett A., 367, 173–176.
  • [10] Déniz, E. G. 2007. A new discrete distribution: Properties and applications in medical care. Journal Applied Statistics, 40(12), 2760–2770.
  • [11] Akdoğan, Y., Kuş, C., Asgharzadeh, A., Kınacı, I., Sharai, F. 2016. Uniform-geometric distribution. Journal of Statistical Computation and Simulation, 86(9), 1754-1770.
  • [12] Kuş, C., Akdoğan, Y., Asgharzadeh, A., Kınacı, İ., and Karakaya, K. 2018. Binomial-discrete Lindley distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 401-411.
  • [13] Kulasekera, K. B. 1994. Approximate MLEs of the Parameters of a Discrete Weibull Distribution with Type I Censored Data. Microelection Reliability, 34, 1185-1188.
  • [14] Gradshteyn, I. S., Ryzhik, I. M. 2007. Table of Integrals, Series, and Products. 7th ed. San Diego, CA: Academic Press, 1171p.
  • [15] Khan, M. S. A., Khalique, A., Abouammoh, A.M. 1989. On estimating parameters in a discrete Weibull distribution. IEEE Transactions on Reliability, 38, 348-350.
  • [16] Weinberg, C. R., Gladen, B. C. 1986. The beta-geometric distribution applied to comparative fecundability studies. Biometrics, 42, 547-560.
  • [17] Xie, M., Goh, T. N. 1993. Improvement detection by control charts for high yield processes. Int J Qual Reliab Manag, 10, 24-31.

Düzgün Geometrik Dağılımının Sansürlü Örneklem Durumunda Parametre Tahmini

Year 2021, Volume: 25 Issue: 1, 49 - 53, 20.04.2021

Mehtap Koca Yunus Akdoğan Kadir Karakaya

https://doi.org/10.19113/sdufenbed.699703

Abstract

Son zamanlarda birçok yeni kesikli dağılım elde edilmiştir. Düzgün geometrik dağılım, yeni elde edilen kesikli bir dağılımdır. Yeni kesikli dağılımlar için sansürlü örneklem durumunda parametre tahmininin eksikliği oldukça fazladır. Bu çalışmada düzgün geometrik dağılımın bilinmeyen parametresi için tip-I sağdan sansürlü örnekleme dayalı parametre tahmini elde edilmiştir. Parametre tahmini en çok olabilirlik yöntemi, oranlar yöntemi, momentler yöntemi ve modifiye edilmiş en çok olabilirlik yöntemleri kullanarak elde edilmiştir. Yöntemlerin parametre tahminindeki performanslarını kıyaslamak için parametre tahminlerinden elde edilen yan ve hata kareler ortalaması Monte Carlo simülasyonu ile elde edilmiştir. Son olarak çalışmada gerçek iki veri uygulaması verilmiştir.

Keywords

Düzgün Geometrik dağılım En çok olabilirlik Modifiye edilmiş en çok olabilirlik Momentler yöntemi Oranlar yöntemi

References

  • [1] Lawless, J. F. 1982. Statistical Models and Methods for Lifetime Data. John Wiley & Sons, New York, 580p.
  • [2] Sinha, S. K. 1986. Reliability and Life testing. Wiley Eastern Ltd, New Delhi, 252p.
  • [3] Nakagawa, T., Osaki, S. 1975. This discrete Weibull distribution. IEEE Transactions on Reliability, 24, 300-301.
  • [4] Stein, W. E., Dattero, R. 1984. A new discrete Weibull distribution. IEEE Transactions on Reliability, 33, 196-197.
  • [5] Roy, D. 2003. The discrete normal distribution. Communications in Statistics Theory and Methods, 32, 1871-1883.
  • [6] Roy, D. 2004. Discrete Rayleigh distribution. IEEE Transactions on Reliability, 53(2), 255-260.
  • [7] Krishna, H., Pundir, P. S. 2009. Discrete Burr and discrete Pareto Distributions. Statistical Methodology, 6, 177-188.
  • [8] Jazi, M. A, Lai, C. D., Alamatsaz, M.H. 2009. A discrete inverse Weibull distribution and estimation of its parameters. Statistical Methodology, 7, 121-132.
  • [9] Hu, Y., Peng, X., Li, T., Guo, H. 2017. On the Poisson approximation to photon distribution for faint lasers. Phys Lett A., 367, 173–176.
  • [10] Déniz, E. G. 2007. A new discrete distribution: Properties and applications in medical care. Journal Applied Statistics, 40(12), 2760–2770.
  • [11] Akdoğan, Y., Kuş, C., Asgharzadeh, A., Kınacı, I., Sharai, F. 2016. Uniform-geometric distribution. Journal of Statistical Computation and Simulation, 86(9), 1754-1770.
  • [12] Kuş, C., Akdoğan, Y., Asgharzadeh, A., Kınacı, İ., and Karakaya, K. 2018. Binomial-discrete Lindley distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 401-411.
  • [13] Kulasekera, K. B. 1994. Approximate MLEs of the Parameters of a Discrete Weibull Distribution with Type I Censored Data. Microelection Reliability, 34, 1185-1188.
  • [14] Gradshteyn, I. S., Ryzhik, I. M. 2007. Table of Integrals, Series, and Products. 7th ed. San Diego, CA: Academic Press, 1171p.
  • [15] Khan, M. S. A., Khalique, A., Abouammoh, A.M. 1989. On estimating parameters in a discrete Weibull distribution. IEEE Transactions on Reliability, 38, 348-350.
  • [16] Weinberg, C. R., Gladen, B. C. 1986. The beta-geometric distribution applied to comparative fecundability studies. Biometrics, 42, 547-560.
  • [17] Xie, M., Goh, T. N. 1993. Improvement detection by control charts for high yield processes. Int J Qual Reliab Manag, 10, 24-31.
There are 17 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehtap Koca This is me 0000-0002-3516-9944

Yunus Akdoğan 0000-0003-3520-7493

Kadir Karakaya 0000-0002-0781-3587

Publication Date April 20, 2021
Published in Issue Year 2021 Volume: 25 Issue: 1

Cite

APA Koca, M., Akdoğan, Y., & Karakaya, K. (2021). Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 25(1), 49-53. https://doi.org/10.19113/sdufenbed.699703
AMA Koca M, Akdoğan Y, Karakaya K. Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample. SDÜ Fen Bil Enst Der. April 2021;25(1):49-53. doi:10.19113/sdufenbed.699703
Chicago Koca, Mehtap, Yunus Akdoğan, and Kadir Karakaya. “Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25, no. 1 (April 2021): 49-53. https://doi.org/10.19113/sdufenbed.699703.
EndNote Koca M, Akdoğan Y, Karakaya K (April 1, 2021) Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25 1 49–53.
IEEE M. Koca, Y. Akdoğan, and K. Karakaya, “Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample”, SDÜ Fen Bil Enst Der, vol. 25, no. 1, pp. 49–53, 2021, doi: 10.19113/sdufenbed.699703.
ISNAD Koca, Mehtap et al. “Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 25/1 (April 2021), 49-53. https://doi.org/10.19113/sdufenbed.699703.
JAMA Koca M, Akdoğan Y, Karakaya K. Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample. SDÜ Fen Bil Enst Der. 2021;25:49–53.
MLA Koca, Mehtap et al. “Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 25, no. 1, 2021, pp. 49-53, doi:10.19113/sdufenbed.699703.
Vancouver Koca M, Akdoğan Y, Karakaya K. Parameter Estimation for Uniform-Geometric Distribution Based on Censored Sample. SDÜ Fen Bil Enst Der. 2021;25(1):49-53.
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