Resampling methods for estimating dispersion indices in random and adaptive designs

In many surveys in environmental and natural phenomena the aim is to evaluate the heterogeneity, and the skewness of the distribution of the number point-objects in the study area opportunely partitioned in sub-regions. For this purpose, in this paper the estimation of dispersion indices is considered by using simple random sampling and adaptive sampling with initial simple random sampling selected with replacement or without replacement. The jackknife and the bootstrap procedures are proposed in both cases for reducing bias. Finally, both a simulation study and a case study on biological population referred to a Oidium tuckeri contamination in a growing vineyard is performed to assess the accuracy of the proposed estimators.