Point and interval estimation of quantiles of several exponential populations with a common location under progressive censoring scheme

Habiba Khatun and Manas Ranjan Tripathy ()
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Habiba Khatun: National Institute of Technology Rourkela
Manas Ranjan Tripathy: National Institute of Technology Rourkela

Computational Statistics, 2024, vol. 39, issue 4, No 20, 2217-2257

Abstract: Abstract We consider the problems of point, and interval estimation of the $$p\textrm{th}$$ p th quantile of the first population when progressive type-II censored samples are available from several exponential populations with a common location, and different scale parameters. First, in the case of point estimation, we derive the maximum likelihood estimator, a modification to it and the uniformly minimum variance unbiased estimator (UMVUE) of the quantile. An estimator dominating the UMVUE is derived. Further, a class of affine equivariant estimators is derived, and an inadmissibility result is proved. Consequently, improved estimators dominating the UMVUE are derived. In the case of interval estimation, several confidence intervals, such as generalized confidence interval, bootstrap confidence interval, and the highest posterior density confidence interval, are obtained for the quantile. The point estimators are compared through the risk values, whereas the interval estimators are compared through coverage probability and average length using a simulation study numerically. The conclusions regarding their performances have been made based on our simulation study. Finally, a real-life data set has been considered for illustrative purposes.

Keywords: Average length; Confidence interval; Coverage probability; Equivariant estimators; Generalized variable method; Inadmissibility; Parametric bootstrap interval; Quadratic loss function; Relative risk performance (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s00180-023-01410-z

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