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Original Articles

Estimation on Lomax progressive censoring using the EM algorithm

, &
Pages 1035-1052 | Received 08 Nov 2012, Accepted 30 Oct 2013, Published online: 25 Nov 2013

References

  • Cohen AC. Progressively censored samples in life testing. Technometrics. 1963;5:327–339. doi: 10.1080/00401706.1963.10490102
  • Mann NR. Best linear invariant estimation for Weibull parameters under progressive censoring. Technometrics. 1971;13:521–533. doi: 10.1080/00401706.1971.10488815
  • Wingo DR. Maximum likelihood estimation of Burr XII distribution parameters under type II censoring. Microelectron Reliab. 1983;23:1251–1257.
  • Balakrishnan N, Sandhu A. A simple simulation algorithm for generating progressive Type-II censored sample. Am Statist. 1995;49:229–230.
  • Aggarwala R, Balakrishnan N. Maximum likelihood estimation of the Laplace parameters based on progressive Type-II censored samples. In: Balakrishnan N, editor. Advances in methods and applications of probability and statistics. Newark, NJ: Gordan and Breach Publisher; 1999. p. 159–167.
  • Balakrishnan N, Asgharzadeh A. Inference for the scaled half-logistic distribution based on progressively Type-II censored samples. Comm Stat Theory Methods. 2005;34:73–87. doi: 10.1081/STA-200045814
  • Balakrishnan N. Progressive censoring methodology: an appraisal (with discussion). TEST 2007;16:211–259. doi: 10.1007/s11749-007-0061-y
  • Lomax K. Business failures; another example of the analysis of failure data. J Am Statist Assoc. 1954;49:847–852. doi: 10.1080/01621459.1954.10501239
  • Chahkandi M, Ganjali M. On some lifetime distributions with decreasing failure rate. Comput Stat Data Anal. 2009;53:4433–4440. doi: 10.1016/j.csda.2009.06.016
  • Bryson MC. Heavy-tailed distributions: properties and tests. Technometrics. 1974;16:61–68. doi: 10.1080/00401706.1974.10489150
  • Arnold BC. The Pareto distributions. Fairland, MD: International Co-operative Publishing House; 1983.
  • Johnson N, Kotz S, Balakrishnan N. Continuous univariate distribution. Vol. 1. New York: John Wiley and Sons; 1994.
  • Childs A, Balakrishnan N, Moshref M. Order statistics from non-identical right-truncated Lomax random variables with applications. Statist Papers. 2001;42:187–206. doi: 10.1007/s003620100050
  • Howlader H, Hossain A. Bayesian survival estimation of Pareto distribution of the second kind based on failure-censored data. Comput Stat Data Anal. 2002;38:301–314. doi: 10.1016/S0167-9473(01)00039-1
  • Elfattah A, Alaboud F, Alharby A. On sample size estimation for Lomax distribution. Aust J Basic Appl Sci. 2007;4:373–378.
  • Asgharzadeh A, Valiollahi R. Estimation of the scale parameter of the Lomax distribution under progressive censoring. Int J Stat Econ. 2011;6:37–48.
  • Raqab MZ, Asgharzadeh A, Valiollahi R. Prediction for Pareto distribution based on progressively Type-II censored samples. Comput Stat Data Anal. 2010;54:1732–1743. doi: 10.1016/j.csda.2010.02.005
  • Cramer E, Schmiedt AB. Progressively type-II censored competing risks data from Lomax distributions. Comput Stat Data Anal. 2011;55:1285–1303. doi: 10.1016/j.csda.2010.09.017
  • Ng HKT, Chan PS, Balakrishnan N. Estimation of parameters from progressively censored data using EM algorithm. Comput Stat Data Anal. 2002;39(4):371–386. doi: 10.1016/S0167-9473(01)00091-3
  • Watanabe M, Yamaguchi K. The EM algorithm and related statistical models. New York: Marcel Dekker; 2004.
  • Rubin DB. Multiple imputation for non-response in surveys. New York: John Wiley; 1987.
  • Tanner MA, Wange WH. The calculation of posterior distributions by data augmentation. J Am Statist Assoc. 1987;82:528–550. doi: 10.1080/01621459.1987.10478458
  • German S, German D. Stochastic relaxation, Gibbs distributions, and Bayesian restoration of images. IEEE Trans Pattern Anal Mach Intell. 1984;6:721–741. doi: 10.1109/TPAMI.1984.4767596
  • Rubin DB. The SIR algorithm. J Am Statist Assoc. 1987;82:543–546.
  • Rubin DB. EM and beyond. Psychometrika. 1991;56:241–254. doi: 10.1007/BF02294461
  • Dempster AP, Laird NM, Rubin DB. Maximum likelihood from incomplete data via the EM algorithm. J R Statist Soc Ser B. 1977;39(1):1–38.
  • Little RJA, Rubin DB. Incomplete data. In: Kotz, S, Johnson NL, editors. Encyclopedia of statistical sciences. Vol. 4. New York: Wiley; 1983. p. 46–53.
  • Balakrishnan N, Aggarwala R. Progressive censoring – theory, methods and applications. Boston, MA: Birkhäuser; 2000.
  • Wang FK, Cheng YF. EM algorithm for estimating the Burr XII parameters with multiple censored data. Qual Reliab Eng Int. 2010;26:615–630. doi: 10.1002/qre.1087
  • McLachlan GJ, Krishnan T. The EM algorithm and extensions. New York: Wiley; 1997.
  • Rud PA. Extensions of estimation methods using the EM algorithm. J Econom. 1991;49:305–341. doi: 10.1016/0304-4076(91)90001-T
  • Jordan M, Xu L. Convergence results for the EM approach to mixtures of experts architectures. Neural Netw. 1996;8:1409–1431. doi: 10.1016/0893-6080(95)00014-3
  • Wu C. On convergence properties of the EM algorithm. Ann Stat. 1983;11:95–103. doi: 10.1214/aos/1176346060
  • Louis TA. Finding the observed information matrix when using the EM algorithm. J R Statist Soc Ser B. 1982;44:226–233.
  • Tanner MA. Tools for statistical inference: observed data and data augmentation methods. 2nd ed. New York: Springer; 1993.
  • Hogg RV, Klugman SA. On the estimation of long-tailed skewed distributions with actuarial applications. J Econom. 1983;23:91–102. doi: 10.1016/0304-4076(83)90077-5
  • Giles D, Feng H, Gadwin R. On the bias of the maximum likelihood estimator for the two parameter Lomax distribution. Comm Stat Theory Methods. 2013;42(11):1934–1950. doi: 10.1080/03610926.2011.600506
  • Simpson J. Use of the gamma distribution in single-cloud rainfall analysis. Monthly Weather Rev. 1972;100:309–312. doi: 10.1175/1520-0493(1972)100<0309:UOTGDI>2.3.CO;2
  • Keating, JP, Mason RL. Practical Relevance of an alternative criterion in estimation. Am Statist. 1985;9:203–205.

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