Inference Based on Type-II Hybrid Censored Data from a Pareto Distribution
DOI:
https://doi.org/10.13052/jrss0974-8024.13243Keywords:
Bayesian inference, maximum-likelihood, Pareto distribution, hybrid censoringAbstract
The Pareto distribution takes part in life-testing experiments as a finite range distribution. In this study, inference studies for the scale and shape parameters of the Pareto distribution under type-II hybrid censoring scheme are considered. The main reason for choosing this censoring scheme is its advantage of guaranteeing at least particular failures to be observed by the end of the experiment. Maximum likelihood and Bayes estimation methods are used with their approximate confidence intervals. Proposed estimation methods are compared numerically based on simulation studies. A numerical example is also used to illustrate the theoretical outcomes.
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References
Abdel-Ghaly, A. A., Attia, A. F., & Aly, H. M. (1998). Estimation of the parameters of pareto distribution and the reliability function using accelerated life testing with censoring. Communications in Statistics-Simulation and Computation, 27(2), 469–484.
Gupta, P. L., & Gupta, R. C. (2000). The monotonicity of the reliability measures of the beta distribution. Applied Mathematics Letters, 13(5), 5–9.
Ghitany, M. E., Kotz, S., & Xie, M. (2005). On some reliability measures and their stochastic orderings for the Topp–Leone distribution. Journal of Applied Statistics, 32(7), 715–722.
Epstein, B. (1954). Truncated life tests in the exponential case. The Annals of Mathematical Statistics, 555–564.
Childs, A., Chandrasekar, B., Balakrishnan, N., Kundu, D. (2003). Exact likelihood inference based on type-I and type-II hybrid censored samples from the exponential distribution. Annals of the Institute of Statistical Mathematics, 55(2), 319–330.
Banerjee, A., & Kundu, D. (2008). Inference based on type-II hybrid censored data from a Weibull distribution. IEEE Transactions on reliability, 57(2), 369–378.
Ganguly, A., Mitra, S., Samanta, D., & Kundu, D. (2012). Exact inference for the two-parameter exponential distribution under Type-II hybrid censoring. Journal of Statistical Planning and Inference, 142(3), 613–625.
Cheng, C., Zhao, H. (2016). Exact inferences of the two-parameter exponential distribution and Pareto distribution with hybrid censored data. Pacific Journal of Applied Mathematics, 8(1), 65.
Fu, J., Xu, A., Tang, Y. (2012). Objective Bayesian analysis of Pareto distribution under progressive Type-II censoring. Statistics and Probability Letters, 82(10), 1829–1836.
Cheng, C., Chen. J., Bai, J. (2013). Exact inferences of the two-parameter exponential distribution and Pareto distribution with censored data. Journal of Applied Statistics, 40(7), 1464–1479.
Balakrishnan, N., Shafay, A.R. (2012). One-and two-sample Bayesian prediction intervals based on Type-II hybrid censored data. Communications in Statistics-Theory and Methods, 41(9), 1511–1531.
Efron, B., Tibshirani, R.J. (1994). An introduction to the bootstrap, CRC press.
Crowder, M. (2000). Tests for a family of survival models based on extremes. In Recent Advances in Reliability Theory (pp. 307–321). Birkhäuser, Boston, MA.
Guan, Q., Tang, Y., & Xu, A. (2013). Objective Bayesian analysis for bivariate Marshall–Olkin exponential distribution. Computational Statistics & Data Analysis, 64, 299–313.
Juvairiyya, R. M., & Anilkumar, P. (2019). Estimation of Stress-Strength Reliability for the Pareto Distribution Based on Upper Record Values. Statistica, 78(4), 397–409.
