Modification of Hansen-Hurwitz's estimators for negatively correlated variates

Most estimators in probability proportional to size (PPS) with replacement (WR) sampling design are defined for positively correlated variables. The literature on estimators involving negatively correlated variates is underdeveloped. This study utilized the law of inverse proportion to derive selection probabilities to modify the Hansen-Hurwitz's estimator for use when negatively correlated variables are encountered in surveys. The suggested estimator is unbiased and could perform better than other estimators when information conveyed by correlation coefficient is used.