The estimation of Simpson's index for a sampling plot

The estimation of the index of Simpson is studied for a sampling plot. The properties of the estimator are developed for a fixed number of observed individuals. Estimators are built for m samples considering two possible structures. The design used is Simple Random Sampling with replacement. The developed estimators are unbiased. Their variances as well as their corresponding estimators are obtained. The behavior of the proposed estimators is studied using the data of an investigation Ordering of Territorial Ecological Classification carried out in the State of Guerrero, Mexico. Experiments of Monte Carlo are developed.