Estimating moments of a selected Pareto population under asymmetric scale invariant loss function

Riyadh Rustam Al-Mosawi () and Shahjahan Khan ()
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Riyadh Rustam Al-Mosawi: Thiqar University
Shahjahan Khan: University of Southern Queensland

Statistical Papers, 2018, vol. 59, issue 1, No 8, 183-198

Abstract: Abstract Consider independent random samples from $$(k\ge 2)$$ ( k ≥ 2 ) Pareto populations with the same known shape parameter but different scale parameters. Let $$X_i$$ X i be the smallest observation of the ith sample. The natural selection rule which selects the population associated with the largest $$X_i$$ X i is considered. In this paper, we estimate the moments of the selected population under asymmetric scale invariant loss function. We investigate risk-unbiased, consistency and admissibility of the natural estimators for the moments of the selected population. Finally, the risk-bias’s and risks of the natural estimators are numerically computed and compared for $$k=2,3.$$ k = 2 , 3 .

Keywords: Pareto distribution; Estimation following selection; Asymmetric scale invariant loss function; Risk unbiased; Primary 62F10; Secondary 62C15; 62F07 (search for similar items in EconPapers)
Date: 2018
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DOI: 10.1007/s00362-016-0758-7

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