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Estimation procedures on Type-II censored data from a scaled Muth distribution

Yıl 2021, Cilt: 39 Sayı: 2, 148 - 158, 02.06.2021

Öz

In the present paper, we consider the estimation problem for the scaled Muth distribution under Type-II censoring scheme. In order to estimate the model parameters α and β, the maximum likelihood, the least-squares, and the maximum spacing estimators are derived. To show estimation efficiencies of the estimators obtained with this paper, we present an extensive Monte-Carlo simulation study in which the estimators are compared according to bias and mean squared error criteria. Furthermore, we evaluate the applicability of the scaled Muth distribution by taking into account both full and Type-II censored data situations by an analysis conducted on a real-life dataset.

Kaynakça

  • [1] Muth E. J. Reliability models with positive memory derived from the mean residual life function. Theory and applications of reliability 1977; 2:401–436.
  • [2] Jodra, P., Jimenez-Gamero, M. D., Alba-Fernandez, M. V. On the Muth distribution. Mathematical Modelling and Analysis 2015; 20(3): 291-310.
  • [3] Balakrishnan, N. Approximate maximum likelihood estimation of the mean and standard deviation of the normal distribution based on type II censored samples. Journal of Statistical Computation and Simulation 1989; 32(3): 137-148.
  • [4] Tiku, M. L., Gill, P. S. Modified maximum likelihood estimators for the bivariate normal based on Type II censored samples. Communications in Statistics-Theory and Methods 1989; 18(9): 3505-3518.
  • [5] Balakrishnan, N., Cutler, C. D. Maximum likelihood estimation of Laplace parameters based on Type-II censored samples. In Statistical Theory and Applications, Springer, New York, 1996 ;p. 145-151.
  • [6] Ng, H. K. T., Kundu, D., Balakrishnan, N. Point and interval estimation for the two-parameter Birnbaum–Saunders distribution based on Type-II censored samples. Computational statistics & data analysis 2006; 50(11): 3222-3242.
  • [7] Kundu, D., Howlader, H. Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data. Computational Statistics & Data Analysis 2010; 54(6): 1547-1558.
  • [8] Kundu, D., Raqab, M. Z. Bayesian inference and prediction of order statistics for a Type-II censored Weibull distribution. Journal of statistical planning and inference 2012; 142(1): 41-47.
  • [9] Okasha, H. M. E-Bayesian estimation for the Lomax distribution based on type-II censored data. Journal of the Egyptian Mathematical Society 2014;22(3): 489-495.
  • [10] Swain, J. J., Venkatraman, S., Wilson, J. R. Least-squares estimation of distribution functions in Johnson's translation system. Journal of Statistical Computation and Simulation 1988; 29(4); 271-297..
  • [11] Lawless, J. F. Statistical models and methods for lifetime data. John Wiley & Sons, New-York, 2011.
  • [12] Cheng, R. C. H., Amin, N. A. K. Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B (Methodological) 1983; 45(3): 394-403.
  • [13] Ranneby, B. The maximum spacing method. An estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics 1984; 11(2): 93-112.
  • [14] Ekström, M. Alternatives to maximum likelihood estimation based on spacings and the Kullback–Leibler divergence. Journal of Statistical Planning and Inference 2008;138(6): 1778-1791.
  • [15] Ng, H. K. T., Luo, L., Hu, Y., Duan, F. Parameter estimation of three-parameter Weibull distribution based on progressively type-II censored samples. Journal of Statistical Computation and Simulation 2012; 82(11): 1661-1678.
  • [16] Proschan F. Theoretical explanation of observed decreasing failure rate. Technometrics 1963; 5(3):375–383.
  • [17] Aarset, M. V. How to identify a bathtub hazard rate. IEEE Transactions on Reliability 1987; 36(1): 106-108.
Yıl 2021, Cilt: 39 Sayı: 2, 148 - 158, 02.06.2021

Öz

Kaynakça

  • [1] Muth E. J. Reliability models with positive memory derived from the mean residual life function. Theory and applications of reliability 1977; 2:401–436.
  • [2] Jodra, P., Jimenez-Gamero, M. D., Alba-Fernandez, M. V. On the Muth distribution. Mathematical Modelling and Analysis 2015; 20(3): 291-310.
  • [3] Balakrishnan, N. Approximate maximum likelihood estimation of the mean and standard deviation of the normal distribution based on type II censored samples. Journal of Statistical Computation and Simulation 1989; 32(3): 137-148.
  • [4] Tiku, M. L., Gill, P. S. Modified maximum likelihood estimators for the bivariate normal based on Type II censored samples. Communications in Statistics-Theory and Methods 1989; 18(9): 3505-3518.
  • [5] Balakrishnan, N., Cutler, C. D. Maximum likelihood estimation of Laplace parameters based on Type-II censored samples. In Statistical Theory and Applications, Springer, New York, 1996 ;p. 145-151.
  • [6] Ng, H. K. T., Kundu, D., Balakrishnan, N. Point and interval estimation for the two-parameter Birnbaum–Saunders distribution based on Type-II censored samples. Computational statistics & data analysis 2006; 50(11): 3222-3242.
  • [7] Kundu, D., Howlader, H. Bayesian inference and prediction of the inverse Weibull distribution for Type-II censored data. Computational Statistics & Data Analysis 2010; 54(6): 1547-1558.
  • [8] Kundu, D., Raqab, M. Z. Bayesian inference and prediction of order statistics for a Type-II censored Weibull distribution. Journal of statistical planning and inference 2012; 142(1): 41-47.
  • [9] Okasha, H. M. E-Bayesian estimation for the Lomax distribution based on type-II censored data. Journal of the Egyptian Mathematical Society 2014;22(3): 489-495.
  • [10] Swain, J. J., Venkatraman, S., Wilson, J. R. Least-squares estimation of distribution functions in Johnson's translation system. Journal of Statistical Computation and Simulation 1988; 29(4); 271-297..
  • [11] Lawless, J. F. Statistical models and methods for lifetime data. John Wiley & Sons, New-York, 2011.
  • [12] Cheng, R. C. H., Amin, N. A. K. Estimating parameters in continuous univariate distributions with a shifted origin. Journal of the Royal Statistical Society: Series B (Methodological) 1983; 45(3): 394-403.
  • [13] Ranneby, B. The maximum spacing method. An estimation method related to the maximum likelihood method. Scandinavian Journal of Statistics 1984; 11(2): 93-112.
  • [14] Ekström, M. Alternatives to maximum likelihood estimation based on spacings and the Kullback–Leibler divergence. Journal of Statistical Planning and Inference 2008;138(6): 1778-1791.
  • [15] Ng, H. K. T., Luo, L., Hu, Y., Duan, F. Parameter estimation of three-parameter Weibull distribution based on progressively type-II censored samples. Journal of Statistical Computation and Simulation 2012; 82(11): 1661-1678.
  • [16] Proschan F. Theoretical explanation of observed decreasing failure rate. Technometrics 1963; 5(3):375–383.
  • [17] Aarset, M. V. How to identify a bathtub hazard rate. IEEE Transactions on Reliability 1987; 36(1): 106-108.
Toplam 17 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Mühendislik
Bölüm Research Articles
Yazarlar

Hayrinisa Demirci Bıçer Bu kişi benim 0000-0002-1520-5004

Berkay Öztürker Bu kişi benim

Yayımlanma Tarihi 2 Haziran 2021
Gönderilme Tarihi 13 Mart 2020
Yayımlandığı Sayı Yıl 2021 Cilt: 39 Sayı: 2

Kaynak Göster

Vancouver Bıçer HD, Öztürker B. Estimation procedures on Type-II censored data from a scaled Muth distribution. SIGMA. 2021;39(2):148-5.

IMPORTANT NOTE: JOURNAL SUBMISSION LINK https://eds.yildiz.edu.tr/sigma/