A family of distance balanced sampling plans

A new family of distanced balanced sampling plans is proposed where second-order inclusion probabilities a non-decreasing function of the distance between the population units. Some properties of the proposed family of sampling plans are studied using Horvitz–Thompson estimator. Relative efficiency of the proposed family is compared with existing sampling plans. Some results on existence and constructions of the proposed family are discussed. Three particular members of the family are studied in detail. Unbiased estimation of variance of Horvitz–Thompson estimator is also possible using the distance balanced sampling plans.