DETERMINATION OF OPTIMUM SAMPLE SIZE AND VARIANCE IN MULTIVARIATE STRATIFIED SAMPLING WITH NON-LINEAR TIME FUNCTION

Abstract

Stratified sample size which determined in Stratified Random Sampling (SRS) with the help of different allocation techniques. The multivariate stratified sampling with linear or nonlinear time function can be optimized using generalized model of time function. After formulation as generalized model with time function (linear or nonlinear), in which the information given that there is only one varying time (time of transportation) and different time involved are constants or insignificant. The formulated generalized model was solved using different techniques but in present paper we use Lagrange multiplier technique to get the optimal solution (i.e. by minimizing the variance) with the involved time constraints. The generalized model with time of transportation is derived under optimum allocation and other involved time is fixed, when the sample size and its variances for a given time is unknown, then different allocation techniques are required for proportionality constant and a given time.