توزیع وایبول-وایبول: برآورد پارامترها تحت سانسور فزایندۀ پیوندی سازوار نوع 2 و پیشبینی واحدهای سانسور شده
Subject Areas : StatisticsAlimohammad Beiranvand 1 , Akram Kohansal 2 , Ramin Kazemi 3 , Farshin Hormozinejad 4
1 - Department of Mathematics and Statistics, Islamic Azad University, Ahvaz Branch, Ahvaz, Iran.
2 - Department of Statistics, Imam Khomeini International University, Qazvin, Iran
3 - Department of Statistics, Imam Khomeini International University,Qazvin, Iran
4 - Department of Mathematics and Statistics, Islamic Azad University, Ahvaz Branch, Ahvaz, Iran.
Keywords: واحدهای سانسور شده, نمونه های سانسور شده, توزیع وایبول-وایبول, برآورد,
Abstract :
The goal of this paper is to study the Weibull-Weibull (WW) distribution under adaptive type-II hybrid progressive censoring, Under this censoring,, the distribution parameters are estimated in the classical and Bayesian methods. Asymptotic distribution of the parameters and asymptotic confidence intervals are introduced. Moreover, two bootstrap confidence intervals are achieved. The Bayesian estimation of the parameters is approximated by using the Markov Chain Monte Carlo (MCMC) algorithm and Lindley's method due to the lack of explicit forms. Furthermore, the highest posterior density (HPD) credible intervals of the parameters are derived. Finally, the different proposed estimations have been compared by the simulation studies. - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
[1] Ahmad, Z., Elgarhy, M., and Hamedani, G.G. 2018. A new Weibull-X family of distributions: properties, characterizations and applications. Journal of Statistical Distributions and Applications 5(5): 1-18.
[2] Cramer, E., and Iliopoulos, G. 2010. Adaptive progressive Type-II censoring. Test 19(2): 342-358.
[3] Dempster, A.P., Laird, N.M., and Rubin, D.B. 1977. Maximum likelihood from incomplete data via the em algorithm. Journal of the Royal Statistical Society, Series B 39(1): 1-38.
[4] Efron, B. 1982. The jackknife, the bootstrap and other re-sampling plans. Philadelphia, PA: SIAM, CBMSNSF Regional Conference Series in Applied Mathematics 34.
[5] Epstein, B. 1954. Truncated life tests in the exponential case. The Annals of Mathematical Statistics 25(3): 555-564.
[6] Hall, P. 1988. Theoretical comparison of bootstrap confidence intervals. Annals of Statistics 16(3): 927-953.
[7] Hashemi, R., and Amiri, L. 2011, Analysis of progressive Type-II censoring in the Weibull model for competing risks data with binomial removals. Applied Mathematical Sciences 5(22): 1073-1087.
[8] Huang, S.R., and Wu, S.J. 2011. Bayesian estimation and prediction for Weibull model with progressive censoring. Journal of Statistical Computation and Simulation 82(11): 1607-1620.
[9] Kaushik, A., Singh, U., and Singh, S.K. 2017. Bayesian Inference for the Parameters of Weibull Distribution under Progressive Type-I Interval Censored Data with Beta-binomial Removals. Communications in Statistics - Simulation and Computation 46(4): 3140-3158.
[10] Kizilaslan, F., and Nadar, M. 2018. Estimation of reliability in a multicomponent stress-strength model based on a bivariate Kumaraswamy distribution. Statistical Papers 59(1): 307-340.
[11] Kizilaslan, F., and Nadar, M. 2016. Estimation and prediction of the Kumaraswamy distribution based on record values and inter-record times. Journal of Statistical Computation and Simulation 86(12): 2471-2493.
[12] Kohansal, A. 2019. On estimation of reliability in a multicomponent stress-strength model for a Kumaraswamy distribution based on progressively censored sample. Statistical Papers 60(6): 2185-2224.
[13] Kohansal, A., and Shoaee, S. 2019. Bayesian and classical estimation of reliability in a multicomponent stress-strength model under adaptive hybrid progressive censored data. Statistical Papers Accepted DOI: 10.1007/s00362-019-01094-y
[14] Lindley, D.V. 1980. Approximate Bayesian methods. Trabajos de Estadistica Y de Investigacion Operativa 31(1): 223-245.
[15] Ng, H.K.T., Kundu, D. and Chan. P.S. 2009. Statistical analysis of exponential lifetimes under an adaptive Type-II progressively censoring scheme. Naval Research Logistics 56(8): 687-698.
[16] Pareek, B., Kundu, D., and Kumar, S. 2009. On progressively censored competing risks data for weibull distributions. Computational Statistics and Data Analysis 53(12), 4083-4094.
[17] Raqab, M.Z., and Nagaraja, H.N. 1995. On some predictors of future order statistics. Metron 53(1-2): 185-204.
[18] Sarhan, A.M., and Al-Ruzaizaa, A. 2010. Statistical inference in connection with the Weibull model using type-II progressively censored data with random scheme. Pakistan Journal of Statistics 26(1): 267-279.
[19] Sultan, K.S., MahMoud, M.R., and Saleh, H.M. 2007. Estimation of parameters of the Weibull distribution based on progressively censored data. International Mathematical Forum 2(41): 2031-2043.
[20] Tse, S.K. and Xiang, L. 2003. Interval estimation for Weibull-distributed life data under type II progressive censoring with random removals. Journal of Biopharmaceutical Statistics 13(1): 1-16.
[21] Tse, S.K., Yang, C., and Yuen, H.K. 2000. Statistical analysis of Weibull distributed lifetime data under Type II progressive censoring with binomial removals. Journal of Applied Statistics 27(8): 1033-1043.
[22] Yuen, H.K., and Tse S.K. 1996. Parameter estimation for Weibull distributed lifetimes under progressive censoring with random removals. Journal of Statistical Computation and Simulation 55(1-2): 57-71.