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.
Fallah, A. (2023). Linear inference for order statistics of Lindley distribution. Journal of Statistical Modelling: Theory and Applications, 4(2), 131-158. doi: 10.22034/jsmta.2024.21542.1140
MLA
Adeleh Fallah. "Linear inference for order statistics of Lindley distribution", Journal of Statistical Modelling: Theory and Applications, 4, 2, 2023, 131-158. doi: 10.22034/jsmta.2024.21542.1140
HARVARD
Fallah, A. (2023). 'Linear inference for order statistics of Lindley distribution', Journal of Statistical Modelling: Theory and Applications, 4(2), pp. 131-158. doi: 10.22034/jsmta.2024.21542.1140
VANCOUVER
Fallah, A. Linear inference for order statistics of Lindley distribution. Journal of Statistical Modelling: Theory and Applications, 2023; 4(2): 131-158. doi: 10.22034/jsmta.2024.21542.1140
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