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

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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.

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Acknowledgements

Our sincere thanks go to the anonymous reviewers for their useful comments and suggestions on an earlier version of the manuscript which led to this improved version.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, McMaster University, Hamilton, ON, L8S 4K1, Canada

    Kai Liu & N. Balakrishnan

  2. Department of Mathematical Sciences, Xi’an Jiaotong-Liverpool University, Suzhou, 215123, Jiangsu Province, People’s Republic of China

    Xiaojun Zhu

Authors
  1. Kai Liu
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  2. Xiaojun Zhu
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  3. N. Balakrishnan
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Correspondence to Kai Liu.

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Liu, K., Zhu, X. & Balakrishnan, N. Exact inference for Laplace distribution under progressive Type-II censoring based on BLUEs. Metrika 81, 211–227 (2018). https://doi.org/10.1007/s00184-017-0640-1

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