Modified Exponential Type Estimator for Population Mean Using Auxiliary Variables in Stratified Random Sampling

Year 2015, , 49 - 56, 30.12.2015

Gamze Özel

https://doi.org/10.17093/aj.2015.3.2.5000145484

Abstract

In this paper, a new exponential type estimator is developed in the stratified random sampling for the population mean using auxiliary variable information. In order to evaluate efficiency of the introduced estimator, we first review some estimators and study the optimum property of the suggested strategy. To judge the merits of the suggested class of estimators over others under the optimal condition, simulation study and real data applications are conducted. The results show that the introduced estimator is more efficient than the available ratio and product estimators, and the conventional unbiased estimator of stratified simple random sampling design.

Tabakalı Rasgele Örneklemede Yardımcı Değişkenler Kullanarak Kitle Ortalaması İçin Değiştirilmiş Üstel Tip Tahmin Edici

Abstract

Bu çalışmada, kitle ortalaması için yardımcı değişken bilgisi kullanarak yeni bir üstel tip tahmin edici tabakalı örneklemede geliştirilmiştir. Elde edilen tahmin edicinin etkinliğini değerlendirebilmek için, ilk olarak literatürdeki bazı tahmin ediciler incelenmiş ve önerilen stratejinin optimum özelliği incelenmiştir. Önerilen tahmin edicinin özelliğini değerlendirebilmek için optimallik koşulu altında benzetim çalışması ve gerçek veri uygulamaları yapılmıştır. Sonuçlar elde edilen tahmin edicinin var olan oran ve çarpım tahmin edicilerinden ve tabakalı örnekleme düzeninde yansız tahmin ediciden daha etkin olduğunu göstermiştir.

References

• Suwattee, P., 2009, Sampling Technique. BKK: Thailand.
• Cochran, W.G., 1977, Sampling Techniques, Third Edition, Wiley Eastern Limited.
• Robson, D.S., 1957, Applications of multivariate polykays to the theory of unbiased ratio type estimation. Journal of American Statistical Association, 52, 511–522.
• Murthy, M.N., 1967, Sampling Theory and Methods, Statistical Publishing Society, Calcutta, India.
• Dianna, G., 1993, A class of estimators of the population mean in stratified random sampling. Statistica, 53, 59-66.
• Kadilar, C., Cingi, H., 2003, Ratio estimators in stratified random sampling. Biometrical Journal, 45, 218-225.
• Singh, H.P., Vishwakarma, G.K., 2005, Combined ratio-product estimator of finite population mean in stratified sampling. Metodologia de Encuesta, 8, 35- 44.
• Singh, H.P., Vishwakarma, G. K., 2008, A family of estimators of population mean using aux-iliary information in stratified sampling. Communication in Statistics Theory and Methods, 37, 1038-1050.
• Singh, R., Chauhan, P., Sawan, N., Smarandache, F. 2009. Improvement in estimating the population mean using exponential estimator in simple random sampling. International Jour-nal of Statistics and Economics, 3, 13-18.
• Bahl, S., Tuteja, R.K., 1991. Ratio and product type exponential estimator. Journal of Infor-mation & Optimization Sciences, 12, 159-163.
• Singh H.P., Vishwakarma, G.K., 2007, Modified exponential ratio and product estimators for finite population mean in double sampling. Austrian Journal of Statistics, 36, 217-225.
• Hansen, M.H., Hurwitz, W.N., Gurney, M. 1946. Problem and methods of the sample survey of business, Journal of American Statistical Association, 41, 174-189.
• Singh, H. P., Tailor, R., Singh, S., Kim, J.M., 2008, A modified estimator of population mean using power transformation, Statistical Papers, 49, 37–58.
• Kadilar, C., Cingi, H., 2005, A new ratio estimator in stratified sampling, Communication in Statistics: Theory and Methods, 34, 597–602.
• Japan Meteorological Society, http://www.data.jma.go.jp/obd/stats/data/en/index.html