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Fisher information based progressive censoring plans

  • Balakrishnan, N.
  • Burkschat, Marco
  • Cramer, Erhard
  • Hofmann, Glenn
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    In life tests, the progressive Type-II censoring methodology allows for the possibility of censoring a number of units each time a failure is observed. This results in a large number of possible censoring plans, depending on the number of both censoring times and censoring numbers. Employing maximum Fisher Information as an optimality criterion, optimal plans for a variety of lifetime distributions are determined numerically. In particular, exact optimal plans are established for some important lifetime distributions. While for some distributions, Fisher information is invariant with respect to the censoring plan, results for other distributions lead us to hypothesize that the optimal scheme is in fact always a one-step method, restricting censoring to exactly one point in time. Depending on the distribution and its parameters, this optimal point of censoring can be located at the end (right censoring) or after a certain proportion of observations. A variety of distributions is categorized accordingly. If the optimal plan is a one-step censoring scheme, the optimal proportion is determined. Moreover, the Fisher information as well as the expected time till the completion of the experiment for the optimal one-step censoring plan are compared with the respective quantities of both right censoring and simple random sampling.

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    File URL: http://www.sciencedirect.com/science/article/B6V8V-4T4HP0W-1/2/1a2d55149eac9cbbd955a2df82767478
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    Article provided by Elsevier in its journal Computational Statistics & Data Analysis.

    Volume (Year): 53 (2008)
    Issue (Month): 2 (December)
    Pages: 366-380

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    Handle: RePEc:eee:csdana:v:53:y:2008:i:2:p:366-380
    Contact details of provider: Web page: http://www.elsevier.com/locate/csda

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    1. Hofmann, Glenn & Balakrishnan, N. & Ahmadi, Jafar, 2005. "Characterization of hazard function factorization by Fisher information in minima and upper record values," Statistics & Probability Letters, Elsevier, vol. 72(1), pages 51-57, April.
    2. An, Mark Yuying, 1995. "Logconcavity versus Logconvexity: A Complete Characterization," Working Papers 95-03, Duke University, Department of Economics.
    3. Balakrishnan, N. & Cramer, E. & Kamps, U., 2001. "Bounds for means and variances of progressive type II censored order statistics," Statistics & Probability Letters, Elsevier, vol. 54(3), pages 301-315, October.
    4. Burkschat, M. & Cramer, E. & Kamps, U., 2006. "On optimal schemes in progressive censoring," Statistics & Probability Letters, Elsevier, vol. 76(10), pages 1032-1036, May.
    5. Zheng, Gang & Gastwirth, Joseph L., 2001. "On the Fisher information in randomly censored data," Statistics & Probability Letters, Elsevier, vol. 52(4), pages 421-426, May.
    6. Gertsbakh, Ilya & Kagan, Abram, 1999. "Characterization of the Weibull distribution by properties of the Fisher information under type-I censoring," Statistics & Probability Letters, Elsevier, vol. 42(1), pages 99-105, March.
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