APPLICATION OF NONLINEAR PROGRAMMING ALGORITHMS TO SOME OPTIMUM STRATIFICATION PROBLEM

Abstract

Mathematical programming is a useful approach in solving the various problems in the statistical fields. In this paper, we will discuss the use of general nonlinear programming algorithms to the determination of the optimum stratification points and minimum variances in the case of estimating the population means for some typical distributions. Three sample allcoations are considered for the normal, exponential, equilateral triangular and rightangled triangular distributions. Efficiency of each sample allocation and gains of the number of strata are examined. Furthermore, relations between the optimum sample size and the number of strata are considered for some cost function. Results obtained here are applicable to the case of repetitive survey.