UNEQUAL ALLOCATION MODELS FOR RANKED SET SAMPLING WITH SKEW DISTRIBUTIONS

Ranked set sampling performs better than simple random sampling when units corresponding to each rank are allocated equally. The performance of ranked set sampling further improves when appropriate unequal allocation is implemented instead of equal allocation. The optimal allocation based on Neyman's approach requires the sample size corresponding to each rank order to be proportional to its standard deviation. In most practical situations, the unavailability of standard deviations of the rank orders makes the optimal allocation impractical. An attempt is made in this paper to make a "near" optimal allocation by exploiting knowledge of other, more easily available, characteristics of the population, like skewness, kurtosis, and coefficient of variation. For positively skewed distributions, it is generally observed that the variances of the rank order statistics increase as the rank orders increase. Thus, it is appropriate to observe ranks corresponding to the right tail more frequently than others. We consider two right-tail allocation models that assign more quantifications to (i) the largest order statistic and (ii) the two largest order statistics. The performance of both the models is better than the equal allocation model and the latter is an improvement over the former under appropriate choices of allocation factors. We study the role played by skewness, kurtosis, and the coefficient of variation for obtaining the allocation factor(s) and also in devising rules-of-thumb. It appears that the coefficient of variation is a better measure to determine the rule-of-thumb.