Linear inference for order statistics of Lindley distribution

Document Type : Original Scientific Paper

Author

Department of Statistics‎, ‎University of Payame Noor‎, ‎Tehran‎, ‎Iran

Abstract

In this paper‎, ‎order statistics and associated inferences are considered from Lindley distribution‎. ‎We derive the exact forms of means‎, ‎variances and covariances as well as the moment generating functions of order statistics‎. ‎These obtained forms allow us to compute the means‎, ‎variances‎, ‎and covariances of the order statistics for various values of the shape parameter‎. ‎These values are then used to compute the coefficients of the best linear unbiased estimators‎, ‎the best linear invariant estimators‎, ‎and the least square estimators of the location and scale parameters‎. ‎The variances and covariances of these estimators are also presented‎. ‎Using the best linear unbiased estimators and best linear invariant estimators we construct confidence intervals for the location and scale parameters through Monte Carlo simulations‎. ‎In addition‎, ‎based on the ordered data‎, ‎we investigate how to obtain the best linear unbiased predictor and the best linear invariant predictor for future order statistics‎. ‎Finally‎, ‎data analysis and Monte Carlo simulation have been performed for illustrative purposes and comparative studies‎, ‎respectively.

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References

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Journal of Statistical Modelling: Theory and Applications
Volume 4, Issue 2
July 2023
Pages 131-158

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History

  • Receive Date: 27 April 2024
  • Revise Date: 09 August 2024
  • Accept Date: 09 September 2024

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