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

Kai Liu (), Xiaojun Zhu () and N. Balakrishnan ()
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Kai Liu: McMaster University
Xiaojun Zhu: Xi’an Jiaotong-Liverpool University
N. Balakrishnan: McMaster University

Metrika: International Journal for Theoretical and Applied Statistics, 2018, vol. 81, issue 2, No 5, 227 pages

Abstract: 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.

Keywords: Best Linear Unbiased Estimators; Confidence interval; Cumulative hazard function; Exact distribution function; Hypoexponential distribution; Laplace distribution; Progressive Type-II censoring; P–P plot; Quantile; Reliability function; Primary 62F10; Secondary 62F86 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00184-017-0640-1

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