Araştırma Makalesi
BibTex RIS Kaynak Göster

Yıl 2019, Cilt: 68 Sayı: 1, 17 - 34, 01.02.2019

Şenay Özdemir Yeşim Güney Yetkin Tuaç Olcay Arslan

https://doi.org/10.31801/cfsuasmas.443579
Cited By: 1

Öz

Kaynakça

  • Al-Hussaini, E. K. and Jaheen, Z. F., Bayes Estimation of the Parameters, Reliability and Failure Rate Functions of the Burr Type XII Failure Model, Journal of Statistical Computation and Simulation (1992), 41 (1-2), 31-40.
  • Al-Saiari, A. Y., Baharith, L. A. and Mousa, S. A., Marshall-Olkin Extended Burr Type XII Distribution, International Journal of Statistics and Probability (2014), 3 (1), 78-84.
  • Burr, W., Cumulative Frequency Functions, The Annals of Mathematical Statistics (1942), 1 (2), 215-232.
  • Caroni, C., Testing for the Marshall--Olkin extended form of the Weibull distribution, Stat. Papers (2010), 51, 325--336.
  • CO₂ emission data for 34 countries access: http://ec.europa.eu/eurostat/tgm/table.do?tab= table&init=1&plugin=1&language=en&pcode=tsdcc100
  • Dogru, F. Z. and Arslan, O., Alternative Robust Estimators for the Shape Parameters of the Burr XII Distribution, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering (2015), 9 (5), 271-276.
  • Ferrari, D. and Yang, Y., Maximum lq-likelihood estimation, The Annals of Statistics (2010), 38, 753--783.
  • Ferrari, D. and Paterlini, S., The maximum lq-likelihood method: an application to extreme quantile estimation in finance, Methodology and Computing in Applied Probability (2009), 11(1), 3--19.
  • Ghitany, M. E., Marshall Olkin Extended Pareto and Its Application, International Journal of Applied Mathematics (2005), 18(1), 17-32.
  • Ghitany, M. E., Al-Hussaini E. K., and AlJarallah.R. A., Marshall--Olkin extended Weibull distribution and its application to censored data, J. Appl. Stat. (2005), 1025--1034.
  • Ghitany, M. E., Al-Awadhi, F. A. and Alkhalfan L. A., Marshall--olkin extended lomax distribution and its application to censored data, Communications in Statistics Theory and Methods (2007), 36(10), 1855-1866.
  • Gui, W., Marshall-Olkin Extended Log-Logistic Distribution and Its Application in Minification Processes, Applied Mathematical Sciences (2013), 7(80), 3947-3961.
  • Gupta, P. L., Gupta, R. C. and Lvin, S. J., Analysis of failure time data by burr distribution, Communications in Statistics-Theory and Methods (1996), 25, 2013-2024.
  • Gupta, R. C., Ghitany, M. E., and Al-Mutairi D. K., Estimation of reliability from Marshall-Olkin extended Lomax distribution, Journal of Statistical Computation and Simulation (2010), 80(8), 937-947.
  • Güney, Y. and Arslan, O., Robust parameter estimation for the Marshall-Olkin extended Burr XII distribution,Commun.Fac.Sci.Univ.Ank.Series A1 (2017), 66(2), 141-161.
  • Havrda, J. and Charv´at, F., Quantification method of classification processes: Concept of structural entropy, Kibernetika (1967), 3, 30--35.
  • Huber, P. J., Robust estimation of a location parameter, Ann. Math. Statist. (1964), 35, 73-101.
  • Klugman, S. A., Loss Distributions, Proceedings of Symposia in Applied Mathematics Actuarial Mathematics (1986), 35, 31-55.
  • Marshall, A. W. and Olkin, I., A new method for adding a parameter to a family of distributions with application to the exponential and weibull families, Biometrika (1997), 84(3), 641-652.
  • McDonald, J. B., Some Generalized Function for the Size Distribution of Income, Econometrica (1984), 52(3), 647-663.
  • Moore, D. and Papadopoulos, A. S., The Burr Type XII Distribution as a Failure Model under Various Loss Functions, Microelectronics Reliability (2000), 40(12), 2117-2122.
  • Papadopoulos, A. S., The Burr Distribution as a Life Time Model from a Bayesian Approach, IEEE Transactions on Reliability (1978), 27(5), 369-371.
  • Qin, Y. and Priebe, C. E., Maximum lq likelihood estimation via the expectation maximization algorithm: A robust estimation of mixture models, Journal of the American Statistical Association (2013), 108(503), 914--928.
  • Ristic, M. M., Jose K. K, and Ancy J., A Marshall--Olkin gamma distribution and minification process, STARS (2007), 11, 107--117.
  • Wu, J., Xing, N. and Liu, S., Maximum Lq-likelihood Estimation for Gamma Distributions, Journal of Advanced Statistics (2017), 2(1), 54-70.

Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution

Yıl 2019, Cilt: 68 Sayı: 1, 17 - 34, 01.02.2019

Şenay Özdemir Yeşim Güney Yetkin Tuaç Olcay Arslan

https://doi.org/10.31801/cfsuasmas.443579
Cited By: 1

Öz

Marshall--Olkin extended Burr XII (MOEBXII) distribution is proposed by Al-Saiari et al. (2014) to obtain a more flexible family of distributions. Some estimation methods like maximum likelihood, Bayes and M estimations are used to estimate the parameters of the MOEBXII distribution  in literature. In this paper, we propose to use Maximum Lq (MLq) estimation method to find alternative estimators for the parameters of the MOEBXII distribution. We give some simulation studies and a real data example to compare the performance of the MLq estimators with the maximum likelihood and M estimators. According to our results MLq estimation method is a good alternative to the maximum likelihood and M estimation methods in the presence of outliers.

Anahtar Kelimeler

Marshall-Olkin extended Burr XII (MOEBXII) distribution maximum Lq estimation maximum likelihood estimator

Kaynakça

  • Al-Hussaini, E. K. and Jaheen, Z. F., Bayes Estimation of the Parameters, Reliability and Failure Rate Functions of the Burr Type XII Failure Model, Journal of Statistical Computation and Simulation (1992), 41 (1-2), 31-40.
  • Al-Saiari, A. Y., Baharith, L. A. and Mousa, S. A., Marshall-Olkin Extended Burr Type XII Distribution, International Journal of Statistics and Probability (2014), 3 (1), 78-84.
  • Burr, W., Cumulative Frequency Functions, The Annals of Mathematical Statistics (1942), 1 (2), 215-232.
  • Caroni, C., Testing for the Marshall--Olkin extended form of the Weibull distribution, Stat. Papers (2010), 51, 325--336.
  • CO₂ emission data for 34 countries access: http://ec.europa.eu/eurostat/tgm/table.do?tab= table&init=1&plugin=1&language=en&pcode=tsdcc100
  • Dogru, F. Z. and Arslan, O., Alternative Robust Estimators for the Shape Parameters of the Burr XII Distribution, International Journal of Mathematical, Computational, Physical, Electrical and Computer Engineering (2015), 9 (5), 271-276.
  • Ferrari, D. and Yang, Y., Maximum lq-likelihood estimation, The Annals of Statistics (2010), 38, 753--783.
  • Ferrari, D. and Paterlini, S., The maximum lq-likelihood method: an application to extreme quantile estimation in finance, Methodology and Computing in Applied Probability (2009), 11(1), 3--19.
  • Ghitany, M. E., Marshall Olkin Extended Pareto and Its Application, International Journal of Applied Mathematics (2005), 18(1), 17-32.
  • Ghitany, M. E., Al-Hussaini E. K., and AlJarallah.R. A., Marshall--Olkin extended Weibull distribution and its application to censored data, J. Appl. Stat. (2005), 1025--1034.
  • Ghitany, M. E., Al-Awadhi, F. A. and Alkhalfan L. A., Marshall--olkin extended lomax distribution and its application to censored data, Communications in Statistics Theory and Methods (2007), 36(10), 1855-1866.
  • Gui, W., Marshall-Olkin Extended Log-Logistic Distribution and Its Application in Minification Processes, Applied Mathematical Sciences (2013), 7(80), 3947-3961.
  • Gupta, P. L., Gupta, R. C. and Lvin, S. J., Analysis of failure time data by burr distribution, Communications in Statistics-Theory and Methods (1996), 25, 2013-2024.
  • Gupta, R. C., Ghitany, M. E., and Al-Mutairi D. K., Estimation of reliability from Marshall-Olkin extended Lomax distribution, Journal of Statistical Computation and Simulation (2010), 80(8), 937-947.
  • Güney, Y. and Arslan, O., Robust parameter estimation for the Marshall-Olkin extended Burr XII distribution,Commun.Fac.Sci.Univ.Ank.Series A1 (2017), 66(2), 141-161.
  • Havrda, J. and Charv´at, F., Quantification method of classification processes: Concept of structural entropy, Kibernetika (1967), 3, 30--35.
  • Huber, P. J., Robust estimation of a location parameter, Ann. Math. Statist. (1964), 35, 73-101.
  • Klugman, S. A., Loss Distributions, Proceedings of Symposia in Applied Mathematics Actuarial Mathematics (1986), 35, 31-55.
  • Marshall, A. W. and Olkin, I., A new method for adding a parameter to a family of distributions with application to the exponential and weibull families, Biometrika (1997), 84(3), 641-652.
  • McDonald, J. B., Some Generalized Function for the Size Distribution of Income, Econometrica (1984), 52(3), 647-663.
  • Moore, D. and Papadopoulos, A. S., The Burr Type XII Distribution as a Failure Model under Various Loss Functions, Microelectronics Reliability (2000), 40(12), 2117-2122.
  • Papadopoulos, A. S., The Burr Distribution as a Life Time Model from a Bayesian Approach, IEEE Transactions on Reliability (1978), 27(5), 369-371.
  • Qin, Y. and Priebe, C. E., Maximum lq likelihood estimation via the expectation maximization algorithm: A robust estimation of mixture models, Journal of the American Statistical Association (2013), 108(503), 914--928.
  • Ristic, M. M., Jose K. K, and Ancy J., A Marshall--Olkin gamma distribution and minification process, STARS (2007), 11, 107--117.
  • Wu, J., Xing, N. and Liu, S., Maximum Lq-likelihood Estimation for Gamma Distributions, Journal of Advanced Statistics (2017), 2(1), 54-70.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Makaleler
Yazarlar

Şenay Özdemir Bu kişi benim 0000-0003-2726-2169

Yeşim Güney 0000-0003-2316-8888

Yetkin Tuaç 0000-0001-6590-3233

Olcay Arslan 0000-0002-7067-4997

Yayımlanma Tarihi 1 Şubat 2019
Gönderilme Tarihi 1 Kasım 2017
Kabul Tarihi 7 Aralık 2017
Yayımlandığı Sayı Yıl 2019 Cilt: 68 Sayı: 1

Kaynak Göster

APA Özdemir, Ş., Güney, Y., Tuaç, Y., Arslan, O. (2019). Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 68(1), 17-34. https://doi.org/10.31801/cfsuasmas.443579
AMA Özdemir Ş, Güney Y, Tuaç Y, Arslan O. Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. Şubat 2019;68(1):17-34. doi:10.31801/cfsuasmas.443579
Chicago Özdemir, Şenay, Yeşim Güney, Yetkin Tuaç, ve Olcay Arslan. “Maximum Lq-Likelihood Estimation for the Parameters of Marshall-Olkin Extended Burr XII Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68, sy. 1 (Şubat 2019): 17-34. https://doi.org/10.31801/cfsuasmas.443579.
EndNote Özdemir Ş, Güney Y, Tuaç Y, Arslan O (01 Şubat 2019) Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68 1 17–34.
IEEE Ş. Özdemir, Y. Güney, Y. Tuaç, ve O. Arslan, “Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., c. 68, sy. 1, ss. 17–34, 2019, doi: 10.31801/cfsuasmas.443579.
ISNAD Özdemir, Şenay vd. “Maximum Lq-Likelihood Estimation for the Parameters of Marshall-Olkin Extended Burr XII Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 68/1 (Şubat 2019), 17-34. https://doi.org/10.31801/cfsuasmas.443579.
JAMA Özdemir Ş, Güney Y, Tuaç Y, Arslan O. Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68:17–34.
MLA Özdemir, Şenay vd. “Maximum Lq-Likelihood Estimation for the Parameters of Marshall-Olkin Extended Burr XII Distribution”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, c. 68, sy. 1, 2019, ss. 17-34, doi:10.31801/cfsuasmas.443579.
Vancouver Özdemir Ş, Güney Y, Tuaç Y, Arslan O. Maximum Lq-Likelihood Estimation for the parameters of Marshall-Olkin Extended Burr XII Distribution. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2019;68(1):17-34.

Cited By

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https://doi.org/10.1007/s00184-020-00774-2

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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