Varied Set Size Ranked Set Sampling with Application to Mean and Ratio Estimation

Varied set size approach of ranked set sampling (VSRSS) is introduced for mean and ratio estimation in situations when balanced ranked set sampling (RSS) cannot be conducted. This approach is used to estimate the total amount of date Oman could produce in 2003. Theoretical and numerical results show that this approach produces an unbiased and more efficient estimator for the population mean and asymptotically unbiased and more efficient estimator for the ratio of two means than using the simple random sample approach. This approach is more practical than the ordinary balance RSS in some real life situation, especially when the population elements are not all available at the time when the study was conducted. However, the entire population elements can be observed as batches of different sizes at different times.