Consider the distribution of Zidiwhere the d.di?s are 1=1 lldifferences independently, identically and symmetrically distributed with mean zero. The problem is to determine properties of the sdd given the distribution of the d.i?fs and the sample size n. The standardized moments as a function of the moments of the d.i!s are developed. A variance reduction technique for estimating the quantiles of the sdd using Monte Carlo methods is developed based on using the randomization sample consisting of the 2nvalues of Zi+d. rather than the single observation i=l lZ d. corresponding to each sample didn. The randomization sample is shown to produce unbiased and consistent estimators.