Open Access Open Access  Restricted Access Subscription or Fee Access

Generalized Exponential Chain Ratio and Chain Product Estimators under Stratified Two-Phase Random Sampling for Non-Response

Aamir Sanaullah, Muhammad Noor ul Amin, Muhammad Hanif, Cem Kadilar


In this paper, some generalized exponential chain-ratio and chain-product estimators have been proposed for estimating the finite population mean under the stratified two-phase random sampling method for two different cases under non-response case when information on only secondary auxiliary variable is available. The expressions for the mean square error (MSE) and bias of the suggested class of estimators have been given for two situations of non-response. The suggested class of generalized exponential estimators has been evaluated in theory with the adapted forms of Hansen-Hurwitz, ratio and product estimators to the stratified two-phase sampling method. Two numerical examples have also been given to demonstrate the performances of the estimators.


Auxiliary Variables, Bias, Mean Square Error, Non-response, Stratified Two-phase Random Sampling, Dependent and Independent Sampling, Exponential Estimator.

Full Text:



  • There are currently no refbacks.

Disclaimer/Regarding indexing issue:

We have provided the online access of all issues and papers to the indexing agencies (as given on journal web site). It’s depend on indexing agencies when, how and what manner they can index or not. Hence, we like to inform that on the basis of earlier indexing, we can’t predict the today or future indexing policy of third party (i.e. indexing agencies) as they have right to discontinue any journal at any time without prior information to the journal. So, please neither sends any question nor expects any answer from us on the behalf of third party i.e. indexing agencies.Hence, we will not issue any certificate or letter for indexing issue. Our role is just to provide the online access to them. So we do properly this and one can visit indexing agencies website to get the authentic information.