In this paper, a nonlinear model is proposed for improving the relationship between the size of a cluster and the variance within the cluster. This model describes the most appropriate functional relation between the within-cluster variance and the cluster size. Through this model, we can obtain the optimum size of a cluster and an estimate of the variance between clusters. The proposed model leads to further improvement in the estimation of the optimum size of a cluster, and the formula for the determination of optimum cluster size leads to explicit solution of models.
Non-linear models, optimum cluster size, four-parameter model, variance function
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