Linear inference for order statistics of Lindley distribution

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Fallah Adeleh

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Journal Paper

Paper Information

Journal: JOURNAL OF STATISTICAL MODELLING: THEORY AND APPLICATIONS Year:2023 | Volume:4 | Issue:2 Page(s): 131-158

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Information Journal Paper

Title

Linear inference for order statistics of Lindley distribution

Author(s)

Fallah Adeleh | Issue Writer Certificate

Keywords

Best linear invariant estimators

Best linear unbiased estimator

Least square estimator

Lindley distribution

Moments of order statistics

prediction

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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