Near Optimal Allocation Model for Skewed Distributions in Ranked Set Sampling

Ranked Set Sampling (RSS) is a useful technique for improving the estimates of mean and variance when the sampling units in a study can be more easily ranked than actual measurements. Under equal allocation, RSS is found to be more precise than simple random sampling (SRS). Further gain in precision of the estimate may be obtained with appropriate use of unequal allocation. For skewed distributions, the optimum gain in precision is obtained through unequal allocation based on Neyman's approach, in which the sample size corresponding to each rank order is proportional to its standard deviation. However, the unavailability of the standard deviations of the rank orders makes the Neyman's approach impractical. Moreover, if the allocation factor(s) are fractional, a number of adjustments are required to make them integers. It is generally observed that the variances of the rank order statistics increase as the rank order increase for positively skewed distributions. In this paper, we used this fact and proposed a “near” optimal allocation model which assigns more measurements to larger order statistics and make each allocation factor(s), if required, integers. The proposed approach performs better than SRS and RSS with equal allocation and quit close to Neyman's allocation in terms of relative precision. We also verified numerically for some skewed distributions.