Comparison of estimators under different loss functions for two-parameter bathtub - shaped lifetime distribution

Yıl 2020, Cilt: 41 Sayı: 3, 602 - 611, 30.09.2020

Gülcan Gencer Kerem Gencer

https://doi.org/10.17776/csj.681535

Öz

Chen is suggested a two-parameter distribution. This distribution can have increasing failure rate function or a bathtub-shaped that allows it to fit real lifetime data sets. The ML (Maximum Likelihood) and Bayes estimates of the parameters of Chen’s distribution are constituted in this paper. The approximate values of Bayesian estimates are obtained by using the Tierney-Kadane approach. Two-parameter bathtub-shaped distribution's estimations are derived using Jeffrey's extension prior under General entropy, Squared and Linex loss functions. Besides, performances of ML and Bayes estimates are compared concerning MSE's (Mean Square Error) by using Monte Carlo simulation. As a result, it has been seen that approximate Bayes estimates obtained under linex loss function are better than others. Moreover, real data analysis for his distribution is presented.

Anahtar Kelimeler

Maximum Likelihood Estimation, Loss Functions, Bayes Estimation, Tierney Kadane's Approximation

Kaynakça

• Chen Z. M., A new two-parameter lifetime distribution with bathtub shape or increasing failure rate function, Statistics & Probability Letters, 49 (2), 2000, 155-161.
• Hjorth U., A reliability distribution with increasing, decreasing, and bathtub-shaped failure rates, Technometrics, 22 (1980) 99–107.
• Mudholkar, G.S. and Srivastava, D.K., Exponentiated Weibull family for analyzing bathtub failure-rate data, IEEE Trans. Rel., 42 (2) 1993 299–302.
• Sarhan A.M., Hamilton D.C. and Smith, B., Parameter estimation for a two-parameter bathtub-shaped lifetime distribution, Applied Mathematical Modelling, 36(11) (2012) 5380-5392.
• Selim M.A., Bayesian Estimations from the Two-Parameter Bathtub-Shaped Lifetime Distribution Based on Record Values, Pakistan Journal of Statistics and Operation Research, 8(2) (2012) 155-165.
• Jung M. and Chung Y., Bayesian inference of three-parameter bathtub-shaped lifetime distribution. Communications in Statistics Theory and Methods, 47(17) (2018) 4229-4241.
• Javadkhan N., Azhdari P. and Azimi R., On Bayesian estimation from two parameter Bathtub-Shaped lifetime distribution based on progressive first-failure-censored sampling, International Journal of Scientific World, 2 (1) (2014) 31-41.
• Faizan M. and Sana, Bayesian Estimation and Prediction for Chen Distribution Based on Upper Record Values, Journal of Mathematics and Statistical Science, 6 ( 2018) 235-243.
• Lee W. C., Wu J. W. and Yu, H. Y., Statistical inference about the shape parameter of the bathtub-shaped distribution under the failure-censored sampling plan, Information and Management Sciences, 18(2) (2007) 157-172.
• Wang F. K., A note on a new two-parameter lifetime distribution with bathtub-shaped failure rate function, International Journal of Reliability and Applications, 3(1) (2002) 51-60.
• Jeffreys H., Theory of Probability, Oxford at the Clarendon Press, 1948.
• Legendre A., Nouvelles M´ethodes pour la D´etermination des Orbites des Com`etes, Paris: Courcier, 1805.
• Gauss C.F., M´ethode des Moindres Carr´es. M´emoire sur la Combination des Observations, Transl. J. Bertrand (1955). Mallet-Bachelier, Paris, 1810.
• Varian H. R., Variants in Economic Theory. Norhampton-USA: Edward Elgar, 2000.
• Zellner A., Bayesian estimation and prediction using asymmetric loss functions, Journal of the American Statistical Association, 81(394) 1986, 446-451.
• Asgharzadeh A., Abdi M. and Wu S.J., Interval estimation for the two-parameter bathtub-shaped lifetime distribution based on records, Hacet. J. Math. Stat., 44 (2015) 399-416.
• Kuş C., A new lifetime distribution, Computational Statistics & Data Analysis, 51 (9) (2007) 4497-4509.
• Karakaya K., Kinaci I., Coşkun K. and Yunus A., A new family of distributions, Hacettepe Journal of Mathematics and Statistics, 46 (2) (2017) 303-314.