ALTERNATE RANKED SET SAMPLING FOR SKEWED AND MOUND SHAPED SYMMETRIC DISTRIBUTIONS: ACCOUNTING FOR FORESTRY AND ENVIRONMENTAL RESEARCH

Raman Nautiyal, Neeraj Tiwari, Girish Chandra, John A. Kershaw, Jr., Trishla Shaktan

Abstract


Ranked Set Sampling (RSS) is a sampling strategy which is advantageous when measurement of sampling units is very difficult but when small sets of units can be ranked according to other methods that do not require actual measurements. The units corresponding to each rank are used in RSS and RSS performs better than simple random sampling (SRS) when estimating the population mean of forestry or environmental parameters (say, below ground biomass). A new RSS procedure based on alternate order statistics for estimating the population mean (ARSS) is suggested in this paper. ARSS measures only the first, third, fifth and so on units so that the information on remaining order statistics is captured from their respective neighboring order statistics. The bias correction term in the proposed estimator is included and calculated for some skewed and symmetric (both mound and U shaped) distributions. The estimators under ARSS are then compared to the estimators based on balanced RSS and Neyman’s optimal unbalanced RSS allocations. Based on the computed Relative Precisions, estimators based on ARSS are recommended for even set sizes of skewed distributions and odd set sizes of mound shaped symmetric distributions. RPs of these distributions are uniformly better than the other two methods (balanced and Neyman’s RSS). To demonstrate the performance of the different estimators, an example from forestry that estimates total biomass of three tree species is presented. The proposed method is efficient in forestry and environmental applications.

Keywords


Above Ground Biomass; Ranked Set Sampling, Relative Precision, Distributions, Unbiasedness

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References


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