Bayesian inference of Unit Gompertz distribution based on dual generalized order statistics

References

• Ahsanullah, M. 2004. Record values–theory and applications. Philadelphia, PA: University Press of America.
   Google Scholar
• Ali, S. 2015. On the Bayesian estimation of the weighted Lindley distribution. Journal of Statistical Computation and Simulation 85 (5):855–80. doi:10.1080/00949655.2013.847442.
   Web of Science ®Google Scholar
• Anwar, Z., N. Gupta, M. A. R. Khan, and Q. A. Jamal. 2020. Recurrence relations for marginal and joint moment generating functions of Topp-Leone generated exponential distribution based on record values and its characterization. Journal of Modern Applied Statistical Methods 18 (1):25. doi:10.22237/jmasm/1571545660.
   Web of Science ®Google Scholar
• Arnold, B. C., N. Balakrishnan, and H. N. Nagaraja. 2008. A first course in order statistics. USA: SIAM.
   Google Scholar
• Arshad, M., and A. Baklizi. 2019. Estimation of common location parameter of two exponential populations based on records. Communications in Statistics - Theory and Methods 48 (6):1545–52. doi:10.1080/03610926.2018.1435805.
   Web of Science ®Google Scholar
• Arshad, M., and Q. A. Jamal. 2019a. Estimation of common scale parameter of several heterogeneous Pareto populations based on records. Iranian Journal of Science and Technology, Transactions A: Science 43 (5):2315–23. doi:10.1007/s40995-019-00689-2.
   Web of Science ®Google Scholar
• Arshad, M., and Q. A. Jamal. 2019b. Interval estimation for Topp-Leone generated family of distributions based on dual generalized order statistics. American Journal of Mathematical and Management Sciences 38 (3):227–40. doi:10.1080/01966324.2018.1509033.
   Google Scholar
• Arshad, M., and Q. A. Jamal. 2019c. Statistical inference for Topp–Leone generated family of distributions based on records. Journal of Statistical Theory and Applications 18 (1):65–78. doi:10.2991/jsta.d.190306.008.
   Web of Science ®Google Scholar
• Azhad, Q. J., M. Arshad, and N. Khandelwal. 2021. Statistical inference of reliability in multicomponent stress strength model for Pareto distribution based on upper record values. International Journal of Modelling and Simulation. Advance online publication. doi:10.1080/02286203.2021.1891496.
   Google Scholar
• Azhad, Q. J., M. Arshad, and A. K. Misra. 2020. Estimation of common location parameter of several heterogeneous exponential populations based on generalized order statistics. Journal of Applied Statistics. Advance online publication. doi:10.1080/02664763.2020.1777395.
   PubMed Web of Science ®Google Scholar
• Caramanis, M., J. Stremel, W. Fleck, and S. Daniel. 1983. Probabilistic production costing: An investigation of alternative algorithms. International Journal of Electrical Power & Energy Systems 5 (2):75–86. doi:10.1016/0142-0615(83)90011-X.
   Web of Science ®Google Scholar
• David, H. A., and H. N. Nagaraja. 2004. Order statistics. Encyclopedia of Statistical Sciences. doi:10.1002/0471667196.ess6023.
   Google Scholar
• Dey, S. 2009. Comparison of Bayes estimators of the parameter and reliability function for Rayleigh distribution under different loss functions. Malaysian Journal of Mathematical Sciences 3 (2):247–64.
   Google Scholar
• El-Din, M. M., and W. Emam. 2018. Prediction intervals for ordinary and dual generalized order statistics from two independent sequences. Communications in Statistics - Simulation and Computation 47 (9):2703–23. doi:10.1080/03610918.2017.1359284.
   Web of Science ®Google Scholar
• Gelman, A., H. S. Stern, J. B. Carlin, D. B. Dunson, A. Vehtari, and D. B. Rubin. 2013. Bayesian data analysis. USA: Chapman and Hall/CRC.
   Google Scholar
• Geman, S., and D. Geman. 1993. Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. Journal of Applied Statistics 20(5–6):25–62. doi:10.1080/02664769300000058.
   Google Scholar
• Gupta, N., and Q. A. Jamal. 2019. Inference for Weibull generalized exponential distribution based on generalized order statistics. Journal of Applied Mathematics and Computing 61 (1-2):573–92. doi:10.1007/s12190-019-01263-0.
   Web of Science ®Google Scholar
• Han, M. 2020. E-Bayesian estimations of the reliability and its E-posterior risk under different loss functions. Communications in Statistics - Simulation and Computation 49 (6):1527–45. doi:10.1080/03610918.2018.1498893.
   Web of Science ®Google Scholar
• Jaheen, Z., and M. M. Al Harbi. 2011. Bayesian estimation based on dual generalized order statistics from the exponentiated Weibull model. Journal of Statistical Theory and Applications 10 (4):591–602.
   Google Scholar
• Jaheen, Z. F. 2003. A Bayesian analysis of record statistics from the Gompertz model. Applied Mathematics and Computation 145 (2-3):307–20. doi:10.1016/S0096-3003(02)00489-7.
   Web of Science ®Google Scholar
• Jha, M. K., S. Dey, R. M. Alotaibi, and Y. M. Tripathi. 2020. Reliability estimation of a multicomponent stress-strength model for Unit Gompertz distribution under progressive Type ii censoring. Quality and Reliability Engineering International 36 (3):965–87. doi:10.1002/qre.2610.
   Web of Science ®Google Scholar
• Jha, M. K., S. Dey, and Y. M. Tripathi. 2020. Reliability estimation in a multicomponent stress–strength based on Unit-Gompertz distribution. International Journal of Quality & Reliability Management 37 (3):428–50. doi:10.1108/IJQRM-04-2019-0136.
   Web of Science ®Google Scholar
• Kamps, U., E. Cramer, and M. Burkschat. 2003. Dual generalized order statistics. Metron 61 (1):13–26.
   Google Scholar
• Khan, M., and M. Arshad. 2016. UMVU estimation of reliability function and stress–strength reliability from proportional reversed hazard family based on lower records. American Journal of Mathematical and Management Sciences 35 (2):171–81. doi:10.1080/01966324.2015.1134363.
   Google Scholar
• Khan, M., and S. Iqrar. 2019. On moments of dual generalized order statistics from Topp-Leone distribution. Communications in Statistics - Theory and Methods 48 (3):479–92. doi:10.1080/03610926.2017.1414260.
   Web of Science ®Google Scholar
• Kim, C., and W. Kim. 2014. Estimation of the parameters of Burr Type III distribution based on dual generalized order statistics. The Scientific World Journal 14:1–6.
   Google Scholar
• Kumar, D., S. Dey, E. Ormoz, and S. MirMostafaee. 2019. Inference for the Unit-Gompertz model based on record values and inter-record times with an application. Rendiconti del Circolo Matematico di Palermo Series 2:1–25.
   Google Scholar
• Lindley, D. V. 1980. Approximate Bayesian methods. Trabajos de Estadistica Y de Investigacion Operativa 31 (1):223–45. doi:10.1007/BF02888353.
   Google Scholar
• Mazucheli, J., A. F. Menezes, and S. Dey. 2019. Unit-Gompertz distribution with applications. Statistica 79 (1):25–43.
   Web of Science ®Google Scholar
• Mazumdar, M., and D. Gaver. 1984. On the computation of power-generating system reliability indexes. Technometrics 26 (2):173–85. doi:10.1080/00401706.1984.10487942.
   Web of Science ®Google Scholar
• Nagamani, N.,. M. R. Tripathy, and S. Kumar. 2021. Estimating common scale parameter of two logistic populations: A Bayesian study. American Journal of Mathematical and Management Sciences 40 (1):44–67. doi:10.1080/01966324.2020.1833794.
   Google Scholar
• Pawlas, P., and D. Szynal. 2001. Recurrence relations for single and product moments of lower generalized order statistics from the inverse Weibull distribution. Demonstratio Math 34 (2):353–58.
   Google Scholar
• Reyad, H. M., A. M. Younis, and S. A. Othman. 2017. E-Bayesian and hierarchical Bayesian estimations based on dual generalized order statistics from the inverse Weibull model. Journal of Advances in Mathematics and Computer Science 23 (1):1–29. doi:10.9734/JAMCS/2017/34540.
   Google Scholar
• Tripathi, A., U. Singh, and S. K. Singh. 2021. Inferences for the DUS-exponential distribution based on upper record values. Annals of Data Science 8 (2):387–403. doi:10.1007/s40745-019-00231-6.
   Google Scholar
• Zhang, F., and W. Gui. 2020. Parameter and reliability inferences of inverted exponentiated half-logistic distribution under the progressive first-failure censoring. Mathematics 8 (5):708–29. doi:10.3390/math8050708.
   Web of Science ®Google Scholar