Ranked set sampling allocation models for skewed variables: an application to agricultural data

The mean of a balanced ranked set sample is more efficient than the mean of a simple random sample of equal size and the precision of ranked set sampling may be increased by using an unbalanced allocation when the population distribution is highly skewed. The aim of this paper is to use the data of the Italian Fifth Agricultural Census driven in year 2000 and of the Italian Farm Structure Survey driven in year 2003 in order to compare several possible allocation rules and to identify the more appropriate one when several skewed distributed attributes of each sample are of interest. Our study shows that when an auxiliary variable correlated with the study variables is available and is used as ranking variable, a multivariate extension of the univariate unequal allocation models suggested for skew distributions by Kaur et al. (1997) may be a good choice.