Sampling from Finite Populations

In this chapter we consider bounds on the expectations of order statistics and their linear combinations for various drawing schemes from finite populations of a given size N. We also determine bounds on variances of order statistics based on sampling from finite populations. In Sect. 5.1, sharp positive upper bounds and negative lower ones for the properly centered L-statistics, expressed in various scale units, based on the standard model of drawing with replacement are presented. A generalization to fixed nonuniform distributions on arbitrary N atoms is presented in Sect. 4.2 . In Sect. 4.3 , we consider analogous problems for the random samples arising from the drawing without replacement models. The last section is devoted to numerical evaluations of expectations of order statistics coming from sample drawings from finite populations determined in this chapter. These bounds are compared with the bounds for order statistics coming from iid samples with arbitrary marginals presented in Chap. 4 .