Abstract
To estimate the variance for rare and cluster population has been the main problemin survey sampling. Three ratio type estimators were proposed for population variance utilizing thesingle auxiliary variable assuming the transformed population for adaptive cluster sampling, inpresented study. The expressions for the mean square error and bias of the proposed estimator werederived. The proposed estimatorswere used to estimate the finite population variance in adaptivecluster sampling. The simulationswereperformedon a real life data to reveal and evaluate the efficiencyof the estimators. The results showed that the proposed exponential ratio estimator was more efficientcompared to the usual sample variance estimator and the proposed ratio type variance estimators inadaptive cluster sampling, assuming given conditions. Hence, exponential ratio estimators wererecommended to estimate the population variance in adaptive cluster sampling.
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