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In this paper, we developed linear exponential (LINEX) loss function by emerging weights to produce weighted linear exponential (WLINEX) loss function. Then we utilized WLINEX to derive scale parameter and reliability function of the Weibull distribution based on record values when the shape parameter is known. After, we estimated scale parameter and reliability function of Weibull distribution by using maximum likelihood (ML) estimation and by several Bayes estimations. The Bayes estimates were obtained with respect to symmetric loss function (squared error loss (SEL)), asymmetric loss function (LINEX) and asymmetric loss function (WLINEX). The ML and the different Bayes estimates are compared via a Monte Carlo simulation study. The result of simulation mentioned that the proposed WLINEX loss function is promising and can be used in real environment especially at the case of underestimate where it revealed better performance than LINEX loss function for estimating scale parameter.
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- Ahsanullah, M. (1980). Linear prediction of record values for the two parameter exponential distribution. Annals of the Institute of Statistical Mathematics, 32(3), 363-368.
- Ahsanullah, M. (1995). Record statistics. Nova Science Publishers.
- Asgharzadeh, A., & Fallah, A. (2010). Estimation and prediction for exponentiated family of distributions based on records. Communications in Statistics—Theory and Methods, 40(1), 68-83.
- Arnold, B. C., Balakrishnan, N. and Nagaraja, H. N. (1998). Records. John Wiley & Sons, New York.Jafari Jozani, M., Marchand, E., Parsian, A. (2006). On estimation with weighted -balanced- type loss function. Statistics & Probability Letters, 76, 773-780.
- Balakrishnan, N., Chan, P. S., & Ahsanullah, M. (1993). Recurrence relations for moments of record values from generalized extreme value distribution. Communications in Statistics-Theory and Methods, 22(5), 1471-1482.
- Basu, A. P., & Ebrahimi, N. (1991). Bayesian approach to life testing and reliability estimation using asymmetric loss function. Journal of statistical planning and inference, 29(1-2), 21-31.
- Nagaraja, H. N. (1988). Record values and related statistics-a review. Communications in Statistics-Theory and Methods, 17(7), 2223-2238.
- Pandey, B. N., & Rai, O. (1992). Bayesian estimation of mean and square of mean of Normal distribution using LINEX loss function. Communications in Statistics-Theory and Methods, 21(12), 3369-3391.
- Shawky, A. I., & Badr, M. M. (2012). Estimations and prediction from the inverse Rayleigh model based on lower record statistics. Life Science Journal, 9(2), 985-990.
- Shojaee, O., Azimi, R., & Babanezhad, M. (2012). Empirical Bayes estimators of parameter and reliability function for compound Rayleigh distribution under record data. American Journal of Theoretical and Applied Statistics, 1(1), 12-15.
- Soliman, A. A., Ellah, A. A., & Sultan, K. S. (2006). Comparison of estimates using record statistics from Weibull model: Bayesian and non-Bayesian approaches. Computational Statistics & Data Analysis, 51(3), 2065-2077.
- Sultan, K. S. (2008). Bayesian estimates based on record values from the inverse Weibull lifetime model. Quality Technology & Quantitative Management, 5(4), 363-374.
- Sultan, K. S., Moshref, M. E., & Abd-El-Hakim, N. S. (2001). Estimation of parameters of Lomax distribution based on record values. The Egyptian Statistical Journal ISSR, 45(2), 135-142.
- Varian, H. R. (1975). A Bayesian approach to real estate assessment. Studies in Bayesian econometric and statistics in Honor of Leonard J. Savage, 195-208.
- Zellner, A. (1986). On assessing prior distributions and Bayesian regression analysis with g-prior distributions. Bayesian inference and decision techniques.