Linear estimation and prediction for the generalized Bilal distribution with application to thermal conductivity data

Akhter Zuber (), Ormoz Ehsan () and MirMostafaee S. M. T. K. ()
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Akhter Zuber: Department of Statistics, University of Delhi, Delhi, India
Ormoz Ehsan: Department of Mathematics and Statistics, Ma. C., Islamic Azad University, Mashhad, Iran
MirMostafaee S. M. T. K.: Department of Statistics, University of Mazandaran, Babolsar, Iran

Monte Carlo Methods and Applications, 2025, vol. 31, issue 4, 357-370

Abstract: This study develops explicit algebraic expressions for the single and product moments of order statistics derived from the generalized Bilal (GB) distribution. These expressions facilitate the computation of means, variances and covariances of order statistics for sample sizes up to n = 10 {n=10} with specified parameter values. The derived moments serve as the foundation for constructing the best linear unbiased estimators (BLUEs) and best linear invariant estimators (BLIEs) for the location and scale parameters applicable to both complete and type-II right censored samples. Additionally, the study explores the prediction of unobserved order statistics in type-II right censored samples. The theoretical results are validated through a simulation study, while a real data example highlights their practical utility. These findings establish a robust framework for statistical inference based on order statistics from the GB distribution.

Keywords: Order statistics; generalized Bilal (GB) distribution; best linear unbiased estimation; prediction; single moments; product moments (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1515/mcma-2025-2018

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