Classical and Bayesian inferential approaches using Lomax model under progressively type-I hybrid censoring. (English) Zbl 1392.62292
Summary: In this article, we consider the problem of estimation and prediction on unknown parameters of a Lomax distribution when the lifetime data are observed in the presence of progressively type-I hybrid censoring scheme. In the classical scenario, the Expectation-Maximization (EM) algorithm is utilized to derive the maximum likelihood estimates (MLEs) for the unknown parameters and associated confidence intervals. Under the Bayesian framework, the point estimates of unknown parameters with respect to different symmetric, asymmetric and balanced loss functions are obtained using Tierney-Kadane’s approximation and Markov Chain Monte Carlo (MCMC) technique. Also, the highest posterior density (HPD) credible intervals for the parameters are reckoned using importance sampling procedure. Simulation experiments are performed to compare the different proposed methods. Further, the predictive estimates of censored observations and the corresponding prediction intervals are also provided. One real-life data example is presented to illustrate the derived results.
MSC:
62N02 | Estimation in survival analysis and censored data |
62F10 | Point estimation |
62F15 | Bayesian inference |
62N05 | Reliability and life testing |
Keywords:
Bayesian estimation; EM algorithm; balanced loss; Tierney-Kadane’s approximation; prediction; progressively type-I hybrid censoringReferences:
[1] | Epstein, B., Truncated life tests in the exponential case, Ann. Math. Statist., 25, 3, 555-564, (1954) · Zbl 0058.35104 |
[2] | Kundu, D.; Joarder, A., Analysis of type-II progressively hybrid censored data, Comput. Statist. Data Anal., 50, 10, 2509-2528, (2006) · Zbl 1284.62605 |
[3] | Cramer, E.; Balakrishnan, N., On some exact distributional results based on type-I progressively hybrid censored data from exponential distributions, Stat. Methodol., 10, 1, 128-150, (2013) · Zbl 1365.62061 |
[4] | Arabi Belaghi, R.; Noori Asl, M., Estimation based on progressively type-I hybrid censored data from the burr XII distribution, Statist. Papers, (2016) · Zbl 1422.62094 |
[5] | Tomer, S. K.; Panwar, M., Estimation procedures for Maxwell distribution under type-I progressive hybrid censoring scheme, J. Stat. Comput. Simul., 85, 2, 339-356, (2015) · Zbl 1457.62323 |
[6] | Chahkandi, M.; Ganjali, M., On some lifetime distributions with decreasing failure rate, Comput. Statist. Data Anal., 53, 12, 4433-4440, (2009) · Zbl 1298.62175 |
[7] | Lomax, K. S., Business failures: another example of the analysis of failure data, J. Amer. Statist. Assoc., 49, 268, 847-852, (1954) · Zbl 0056.13702 |
[8] | Balakrishnan, N.; Aggarwala, R., Progressive censoring: theory, methods, and applications, (2000), Springer New York |
[9] | Marshall, A. W.; Olkin, I., Life distributions, structure of nonparametric, semiparametric, and parametric families, (2007), Springer New York · Zbl 1304.62019 |
[10] | Cramer, E.; Schmiedt, A. B., Progressively type-II censored competing risks data from Lomax distribution, Comput. Statist. Data Anal., 55, 1285-1303, (2011) · Zbl 1328.65025 |
[11] | Helu, A.; Samawi, H.; Raqab, M. Z., Estimation on Lomax progressive censoring using the EM algorithm, J. Stat. Comput. Simul., (2013) |
[12] | Dempster, A. P.; Laird, N. M.; Rubin, D. B., Maximum likelihood from incomplete data via the EM algorithm, J. Roy. Statist. Soc. Ser. B, 1-38, (1977) · Zbl 0364.62022 |
[13] | Louis, T. A., Finding the observed information matrix when using the EM algorithm, J. R. Stat. Soc. Ser. B Stat. Methodol., 226-233, (1982) · Zbl 0488.62018 |
[14] | Lawless, J. F., Statistical models and methods for lifetime data, (2003), Wiley Hoboken · Zbl 1015.62093 |
[15] | Varian, H. R., A Bayesian approach to real estate assessment, (Studies in Bayesian Econometrics & Statistics in Honor of Leonard J. Savage, (1975)), 195-208 |
[16] | Tierney, L.; Kadane, J. B., Accurate approximations for posterior moments and marginal densities, J. Amer. Statist. Assoc., 81, 393, 82-86, (1986) · Zbl 0587.62067 |
[17] | Chen, M. H.; Shao, Q. M., Monte Carlo estimation of Bayesian credible and hpd intervals, J. Comput. Graph. Statist., 8, 1, 69-92, (1999) |
[18] | Raqab, M.; Nagaraja, H., On some predictors of future order statistics, Metron, 53, 1-2, 185-204, (1995) · Zbl 0883.62047 |
[19] | Singh, S.; Tripathi, Y. M., Bayesian estimation and prediction for a hybrid censored lognormal distribution, IEEE Trans. Reliab., 65, 2, 782-795, (2016) |
[20] | Hogg, R. V.; Klugman, S. A., On the estimation of long-tailed skewed distributions with actuarial applications, J. Econom., 23, 91-102, (1983) |
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