Generalized exponential type estimator of population mean in the presence of non-response

Siraj  Muneer; Javid  Shabbir; Alamgir  Khalil

doi:https://doi.org/10.21307/stattrans-2018-015

Generalized exponential type estimator of population mean in the presence of non-response

Siraj Muneer Department of Statistics, University of Peshawar, Peshawar, Pakistan. , Javid Shabbir Department of Statistics, Quaid-i-Azam University, Islamabad, Pakistan. , Alamgir Khalil Department of Statistics, University of Peshawar, Peshawar, Pakistan. Statistics in Transition new series, vol. 19, 2018, 2, pages: 259-276 Published online: 1 June 2018 https://doi.org/10.21307/stattrans-2018-015

219 Views 12 Downloads

ARTICLE

(English) PDF

ABSTRACT

In this article, we propose a class of generalized exponential type estimators to estimate the finite population mean by using two auxiliary variables under non-response in simple random sampling. The proposed estimator under non-response in different situations has been studied and gives minimum mean square error as compared to all other considered estimators. Usual exponential ratio type estimator, exponential product type estimator and many more estimators are also identified from the proposed estimator. We use three real data sets to obtain the efficiencies of estimators.

KEYWORDS

auxiliary variables, bias, MSE, efficiency, non-response.

REFERENCES

BAHL, S., TUTEJA, R, K., (1991). Ratio and product type exponential estimator.Information and Optimization Sciences. 12, pp. 159–163.

EL-BADRY, M. A., (1956). A sampling procedure for mailed questionnaires. J.Amer. Statist. Assoc. 51, pp. 209–227.

HANSEN, M. H., HURWITZ, W. N., (1946). The problem of non-response in sam pling surveys. Journal of American Statistical Association. 41, pp. 517–529.

ISMAIL, M., SHAHBAZ, M. S., HANIF, M., (2011). A general class of estimator of population mean in presence of non-response. Pakistan Journal of Statistics.27 (4), pp. 467–476.

KHARE, B. B., SRIVASTAVA, S. R., (1981). A generalized regression ratio estima tor for the population mean using two auxiliary variables. The Aligarh Journal of Statistics. 1(1), pp. 43–51.

KHARE, B. B., SRIVASTAVA, S., (1993). Estimation of population mean using aux iliary character in presence of non-response. Nat. Acad. Sci. Lett. India. 16,pp. 111–114.

KHARE, B. B., SRIVASTAVA, S., (1995). Study of conventional and alternative two-phase sampling ratio, product and regression estimators in presence of non-response. Nat. Acad. Sci. Lett. India. 65, pp. 195–203.

KHARE, B. B., SRIVASTAVA, S., (1997). Transformed ratio type estimators for the population mean in presence of non-response. Communication in Statistics Theory and Method. 17, pp. 1779–1791.

KHARE, B. B., SRIVASTAVA, S., (2010). Generalized two phase estimators for the population mean in the presence of non-response. The Aligarh journal of Statistics. 30, pp. 39–54.

KHARE, B. B., SINHA, R, R., (2007). Estimation of the ratio of the two population means using multi auxiliary characteristics in the presence of non-response.In Statistical Techniques in Life Testing, Reliability, Sampling Theory and Qual ity Control. 1, pp. 63–171.

KHARE, B. B., SINHA, R, R., (2009). On the class of estimators for popula tion mean using multi auxiliary characters in the presence of non-response.Statistics in Transition-New Series. 10 (1), pp. 3–14.

Khare, B. B., Sinha, R, R., (2012). Improved classes of estimators for ratio of two means with with double sampling the non-respondents. Statistica. 49 (3), pp.75–83.

KUMAR, S., BHOUGAL, S., (2011). Estimation of the population mean in pres ence of non-response. Communications of the Korean Statistical Society. 18 (4), pp. 537–548.

MUNEER, S., SHABBIR, J, KHALIL, A., (2017). Estimation of finite population mean in simple random sampling and stratified random sampling using two auxiliary variables. Communication in Statistics Theory and Methods. 46 (5),pp. 2181–2192.

RAO, P. S. R. S., (1986). Ratio estimation with sub sampling the non-respondents. Survey Methodology. 12 (2), pp. 217–230.

OLKIN, I., (1958). Multivariate ratio estimation for finite populations. Biometrika, 45, pp. 154–165.

SINGH, H. P., KUMAR, S., (2008). A regression approach to the estimation of the finite population mean in the presence of non-response. Aust. N. Z. J. Stat.50(4), pp. 395–408.

SINGH, H. P., KUMAR, S., KOZAK, M., (2010) Improved estimation of finite popu lation mean using sub-sampling to deal with non response in two phase sam pling scheme. Communication in Statistics Theory and Method. 39 (5), pp. 791–802.

SRINATH, K. P., (1971). Multiphase sampling in non-response problems. Journal of American Statistical Association. 66, pp. 583–586.

SHABBIR, J., NASIR, S., (2013). On estimating the finite population mean using two auxiliary variables in two phase sampling in the presence of non response.Communication in Statistics-Theory and Methods. 42, pp. 4127–4145.

SHUKLA, D., PATHAK, S., THAKUR, N. S., (2012) A transformed estimator for es timation of population mean with missing data in sample surveys. Journal of current engineering research. 2 (1):50-55.

SINGH, V. K., SHUKLA, D., (1993) An efficient one parameter family of factor-type estimator in sample survey. Metron. 51 (1-2), pp. 139–159.

TABASUM, R., KHAN, I. A., (2006). Double sampling for ratio estimator for the population mean in the presence of non-response. Assam Statistical Review 20, pp. 73–83.