Bayesian Estimation for the Two Log-Logistic Models Under Joint Type II Censoring Schemes
DOI:
https://doi.org/10.13052/jrss0974-8024.15110Keywords:
Log-logistic model, Bayes estimation, Joint type II censoring scheme, Bayesian credible interval, Markov Chain Monte CarloAbstract
The present paper, discusses classical and Bayesian estimation of unknown combined parameters of two different log-logistic models with common shape parameters and different scale parameters under a new type of censoring scheme known as joint type II censoring scheme. Maximum likelihood estimators are derived. Bayes estimates of parameters are proposed under different loss functions. Classical asymptotic confidence intervals along with the Bayesian credible intervals and Highest Posterior Density region are also constructed. Markov Chain Monte Carlo approximation method is used for simulating the theoretic results. Comparative assessment of the classical and the Bayes results are illustrated through a real archived dataset.
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Abdel-Aty, Y. (2017). Exact likelihood inference for two populations from two-parameter exponential distributions under joint Type-II censoring. Communications in Statistics-Theory and Methods, 46(18), 9026–9041.
Ahsanullah, M., and Alzaatreh, A. (2018). Parameter estimation for the log-logistic distribution based on order statistics. REVSTAT, 16(4), 429–443.
Aldrich, J. (1997). RA Fisher and the making of maximum likelihood 1912–1922. Statistical Science, 12(3), 162–176.
Al-Matrafi, B. N., and Abd-Elmougod, G. A. (2017). Statistical inferences with jointly type-II censored samples from two rayleigh distributions. Global Journal of Pure and Applied Mathematics, 13(12), 8361–8372.
Al-Shomrani, A. A., Shawky, A. I., Arif, O. H., and Aslam, M. (2016). Log-logistic distribution for survival data analysis using MCMC. SpringerPlus, 5(1), 1–16.
Ashkar, F., and Mahdi, S. (2006). Fitting the log-logistic distribution by generalized moments. Journal of Hydrology, 328(3–4), 694–703.
Ashour, S. K., and Abo-Kasem, O. E. (2014). Parameter estimation for two Weibull populations under joint Type II censored scheme. International Journal of Engineering, 5(04), 8269.
Ashour, S. K., and Abo-Kasem, O. E. (2014). Bayesian and non–Bayesian estimation for two generalized exponential populations under joint type II censored scheme. Pakistan Journal of Statistics and Operation Research, 57–72.
Balakrishnan, N., and Rasouli, A. (2008). Exact likelihood inference for two exponential populations under joint Type-II censoring. Computational Statistics & Data Analysis, 52(5), 2725–2738.
Balakrishnan, N., and Su, F. (2015). Exact likelihood inference for k exponential populations under joint type-II censoring. Communications in Statistics-Simulation and Computation, 44(3), 591–613.
Berger, J. O. (1985). Prior information and subjective probability. In Statistical Decision Theory and Bayesian Analysis (pp. 74–117). Springer, New York, NY.
Calabria, R., and Pulcini, G. (1996). Point estimation under asymmetric loss functions for left-truncated exponential samples. Communications in Statistics-Theory and Methods, 25(3), 585–600.
Chehade, A., Shi, Z., and Krivtsov, V. (2020). Power–law nonhomogeneous Poisson process with a mixture of latent common shape parameters. Reliability Engineering & System Safety, 203, 107097.
Collett, D. (2015). Modelling survival data in medical research. CRC press.
Fisk, P. R. (1961). The graduation of income distributions. Econometrica: journal of the Econometric Society, 171–185.
Guure, C. B. (2015). Inference on the loglogistic model with right censored data. Austin Biom and Biostat, 2(1), 1015.
Hastings, W. K. (1970). Monte Carlo sampling methods using Markov chains and their applications. Biometrika, 57(1), 97–109.
Hoel, D. G. (1972). A representation of mortality data by competing risks. Biometrics, 475–488.
Islam, A. F. M., Roy, M. K., and Ali, M. M. (2004). A Non-Linear Exponential (NLINEX) Loss Function in Bayesian Analysis. Journal of the Korean Data and Information Science Society, 15(4), 899–910.
Jeffreys, H. (1961). Theory of probability: Oxford university press. New York, 472.
Lawless, J. F. (2003). Copyright© 2003 John Wiley & Sons, Inc. Statistical Models and Methods for Lifetime Data, 3, 577.
Metropolis, N., A.W. Rosenbluth, M.N. Rosenbluth, A.H. Teller and E. Teller. (1953). Equation of state calculations by fast computing machines. Journal of Chemical Physics, 21(6): 1087–1091. DOI: 10.1063/1.1699114
Nelson, W. B. (2003). Recurrent Events Data Analysis for Product Repairs, Disease Recurrences, and Other Applications. Society for Industrial and Applied Mathematics.
Nelson, W. B. (2009). Accelerated Testing: Statistical Models, Test Plans, and Data Analysis (Vol. 344). John Wiley & Sons.
Panza, C. A., and Vargas, J. A. (2016). Monitoring the shape parameter of a Weibull regression model in phase II processes. Quality and Reliability Engineering International, 32(1), 195–207.
Reath, J., Dong, J., and Wang, M. (2018). Improved parameter estimation of the log-logistic distribution with applications. Computational Statistics, 33(1), 339–356.
Sewailem, M. F., and Baklizi, A. (2019). Inference for the log-logistic distribution based on an adaptive progressive type-II censoring scheme. Cogent Mathematics & Statistics, 6(1), 1684228.
Singh, V. P., and Guo, H. (1995). Parameter estimation for 2-parameter log-logistic distribution (LLD2) by maximum entropy. Civil Engineering Systems, 12(4), 343–357.
Shafay, A. R., Balakrishnan, N., and Abdel-Aty, Y. (2014). Bayesian inference based on a jointly type-II censored sample from two exponential populations. Journal of Statistical Computation and Simulation, 84(11), 2427–2440.
Shoukri, M. M., Mian, I. U. H., and Tracy, D. S. (1988). Sampling properties of estimators of the log-logistic distribution with application to Canadian precipitation data. Canadian Journal of Statistics, 16(3), 223–236.
Tripathy, M. R., and Nagamani, N. (2017). Estimating common shape parameter of two gamma populations: A simulation study. Journal of Statistics and Management Systems, 20(3), 369–398.
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.
Voorn, W. J. (1987). Characterization of the logistic and loglogistic distributions by extreme value related stability with random sample size. Journal of Applied Probability, 24(4), 838–851.
