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Exact inference for Laplace distribution under progressive Type-II censoring based on BLUEs

Author

Listed:
  • Kai Liu

    (McMaster University)

  • Xiaojun Zhu

    (Xi’an Jiaotong-Liverpool University)

  • N. Balakrishnan

    (McMaster University)

Abstract

In this paper, upon using the known expressions for the Best Linear Unbiased Estimators (BLUEs) of the location and scale parameters of the Laplace distribution based on a progressively Type-II right censored sample, we derive the exact moment generating function (MGF) of the linear combination of standard Laplace order statistics. By using this MGF, we obtain the exact density function of the linear combination. This density function is then utilized to develop exact marginal confidence intervals (CIs) for the location and scale parameters through some pivotal quantities. Next, we derive the exact density of the BLUEs-based quantile estimator and use it to develop exact CIs for the population quantile. A brief mention is made about the reliability and cumulative hazard functions and as to how exact CIs can be constructed for these functions based on BLUEs. A Monte Carlo simulation study is then carried out to evaluate the performance of the developed inferential results. Finally, an example is presented to illustrate the point and interval estimation methods developed here.

Suggested Citation

  • Kai Liu & Xiaojun Zhu & N. Balakrishnan, 2018. "Exact inference for Laplace distribution under progressive Type-II censoring based on BLUEs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 81(2), pages 211-227, February.
    • Handle: RePEc:spr:metrik:v:81:y:2018:i:2:d:10.1007_s00184-017-0640-1
    DOI: 10.1007/s00184-017-0640-1
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    References listed on IDEAS

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    1. N. Balakrishnan, 2007. "Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 211-259, August.
    2. Balakrishnan, N. & Kundu, Debasis, 2013. "Hybrid censoring: Models, inferential results and applications," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 166-209.
    3. N. Balakrishnan, 2007. "Rejoinder on: Progressive censoring methodology: an appraisal," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(2), pages 290-296, August.
    4. Iliopoulos, G. & Balakrishnan, N., 2009. "Conditional independence of blocked ordered data," Statistics & Probability Letters, Elsevier, vol. 79(8), pages 1008-1015, April.
    5. Childs, Aaron & Balakrishnan, N., 1996. "Conditional inference procedures for the Laplace distribution based on Type-II right censored samples," Statistics & Probability Letters, Elsevier, vol. 31(1), pages 31-39, December.
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