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A Theoretical Inference About Ratio Estimation of Population Mean Using Ranked Set Sampling Under Bivariate Normal Distribution

Year 2020, Volume: 9 Issue: 4, 1469 - 1481, 25.12.2020
https://doi.org/10.17798/bitlisfen.688795

Abstract

Ranked set sampling is a sampling technique that uses ranking information when measuring units is difficult or expensive. In this study, ratio estimation of the population mean is considered in the case of units ranking by both auxiliary variable and the variable of interest in ranked set sampling under bivariate normal distribution. We obtained some theoretical inferences about the mean square error of the ratio estimation in this situation in a simple form depending on coefficient of variation. Besides, we made a theoretical comparison of mean square errors by ranking based on auxiliary variable and interested variable. Using this comparison, one can choose which ranking strategy should be utilized in a problem easily. The performance of the ratio estimators was compared by a simulation study. The simulation results indicated that the ranked set sampling estimators were more efficient than the simple random sampling estimators for the same sample size and correlation coefficient. A real data example was also given to demonstrate for calculating relative efficiencies.

References

  • Dell D.R., Clutter J.L. 1972. Ranked set sampling theory with order statistics background. Biometrics, 28, 545-555.
  • McIntyre G.A. 1952. A method of unbiased selective sampling using ranked sets, Australian Journal of Agricultural Reseach, 3, 385-390.
  • Takahasi K., Wakimoto K. 1968. On Unbiased Estimates of the Population Mean Based on the Sample Stratified by Means of Ordering. Annals of the Institute of Statistical Mathematics, 20, 1-31.
  • Lam K., Sinha B.K., Wu Z. 1994. Estimation of parameters in two parameters exponential distribution using ranked set sample. Annals of the Institute of Statistical Mathematics, 46, 723-736.
  • Sinha, Bimal. K., Sinha, Bikas K., Purkayastha S. 1996. On some aspects of ranked set sampling for estimation of normal and exponential parameters. Statistical Decisions, 14, 223-240.
  • Bhoj D.S., Ahsanullah M. 1996. Estimation of parameters of the generalized geometric distribution using ranked set sampling. Biometrics, 52, 685-694.
  • Ozturk O. 2011. Parametric estimation of location and scale parameters in ranked set sampling, Journal of Statistical Planning and Inference, 141 (4), 1616-1622.
  • Tahmasebi S., Jafari A.A. 2014. Estimators for the parameter mean of Morgenstern type bivariate generalized exponential distribution using Rayleigh distribution revisited via ranked set sampling, Sort –Statistics and Operations Research Transactions, 38(2), 161-179.
  • Dey S., Salehi M., Ahmadi J. 2017. RayleighRayleigh distribution revisited via ranked set sampling, Metron-International Journal of Statistics, 75(1), 69-85.
  • Ozturk O., Demirel N. 2016. Estimation of Population Variance from Multi-Ranker Ranked Set Sampling Designs. Communications in Statistics-Simulation and Computation, 45(10), 3568-3583.
  • Samawi H. M., Muttlak H.A. 1996. Estimation of ratio using rank set sampling. Biometrical Journal, 38(6), 753-764.
  • Ganeslingam S., Ganesh S. 2006. Ranked set sampling versus simple random sampling in the estimation of the mean and the ratio. Journal of Statistics and Management Systems, 9(2), 459-472.
  • Al-Omari A.I., Jaber K., Al-Omari A. 2008. Modified ratio-type estimators of the mean using extreme ranked set sampling. Journal of Mathematics and Statistics, 4(3), 150-155.
  • Al-Omari A.I., Jemain A.A., Ibrahim K. 2009. New ratio estimators of the mean using simple random sampling and ranked set sampling methods. Investigación Operacional, 30(2), 97-108.
  • Kadılar C., Ünyazıcı Y., Çıngı H. 2009. Ratio estimator for the population mean using ranked set sampling. Statistical Papers, 50(2), 301-309.
  • Al-Omari A.I. 2012. Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling. Statistics and Probability Letters, 82(11), 1883-1890.
  • Singh H.P., Tailor R., Singh S. 2014. General procedure for estimating the population mean using ranked set sampling. Journal of Statistical Computation and Simulation, 84(5), 931-945.
  • Ozturk, O. 2018. Ratio estimators based on a ranked set sample in a finite population setting. Journal of the Korean Statistical Society, 47, 226-238.
  • Stokes L. S. 1977. Ranked set sampling with concomitant variables. Commun. Statist. Theor. Meth., A6(12), 1207-1211.
  • Bütün S. 2013. Keban Baraj Gölü’nde Yaşayan Alburnus Mossulensis Heckel, 1843’de Otolit Biyometrisi, Fırat Üniversitesi Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, Elazığ, 4-30.

A Theoretical Inference About Ratio Estimation of Population Mean Using Ranked Set Sampling Under Bivariate Normal Distribution

Year 2020, Volume: 9 Issue: 4, 1469 - 1481, 25.12.2020
https://doi.org/10.17798/bitlisfen.688795

Abstract

Sıralı küme örneklemesi, birimleri ölçmenin zor veya pahalı olduğu durumlarda sıralama bilgisini kullanan bir örnekleme tekniğidir. Bu çalışmada, iki değişkenli normal dağılım altında sıralı küme örneklemesinde hem yardımcı değişken hem de ilgilenilen değişkene göre birimlerin sıralaması söz konusu olduğunda yığın ortalamasının oran tahmini dikkate alınmıştır. Bu durumda oran tahmininin hata kare ortalamasına ilişkin değişim katsayısına bağlı bazı teorik çıkarımlar elde edilmiştir. Ayrıca, yardımcı değişken ve ilgili değişkene göre sıralama yapılarak elde edilen ortalama hata karelerin teorik bir karşılaştırması yapılmıştır. Bu karşılaştırma kullanılarak, ele alınan problemde hangi sıralama stratejisinin kullanılması gerektiği kolayca seçilebilir. Oran tahmin edicilerinin performansı bir simülasyon çalışması ile karşılaştırılmıştır. Simülasyon sonuçları, aynı örnek büyüklüğü ve korelasyon katsayısı için sıralı küme örneklemesi tahmin edicilerinin, basit rastgele örnekleme tahmin edicilerinden daha etkin olduğunu göstermiştir. Göreli etkinliklerin hesaplanmasını göstermek için gerçek veri örneği de sunulmuştur.

References

  • Dell D.R., Clutter J.L. 1972. Ranked set sampling theory with order statistics background. Biometrics, 28, 545-555.
  • McIntyre G.A. 1952. A method of unbiased selective sampling using ranked sets, Australian Journal of Agricultural Reseach, 3, 385-390.
  • Takahasi K., Wakimoto K. 1968. On Unbiased Estimates of the Population Mean Based on the Sample Stratified by Means of Ordering. Annals of the Institute of Statistical Mathematics, 20, 1-31.
  • Lam K., Sinha B.K., Wu Z. 1994. Estimation of parameters in two parameters exponential distribution using ranked set sample. Annals of the Institute of Statistical Mathematics, 46, 723-736.
  • Sinha, Bimal. K., Sinha, Bikas K., Purkayastha S. 1996. On some aspects of ranked set sampling for estimation of normal and exponential parameters. Statistical Decisions, 14, 223-240.
  • Bhoj D.S., Ahsanullah M. 1996. Estimation of parameters of the generalized geometric distribution using ranked set sampling. Biometrics, 52, 685-694.
  • Ozturk O. 2011. Parametric estimation of location and scale parameters in ranked set sampling, Journal of Statistical Planning and Inference, 141 (4), 1616-1622.
  • Tahmasebi S., Jafari A.A. 2014. Estimators for the parameter mean of Morgenstern type bivariate generalized exponential distribution using Rayleigh distribution revisited via ranked set sampling, Sort –Statistics and Operations Research Transactions, 38(2), 161-179.
  • Dey S., Salehi M., Ahmadi J. 2017. RayleighRayleigh distribution revisited via ranked set sampling, Metron-International Journal of Statistics, 75(1), 69-85.
  • Ozturk O., Demirel N. 2016. Estimation of Population Variance from Multi-Ranker Ranked Set Sampling Designs. Communications in Statistics-Simulation and Computation, 45(10), 3568-3583.
  • Samawi H. M., Muttlak H.A. 1996. Estimation of ratio using rank set sampling. Biometrical Journal, 38(6), 753-764.
  • Ganeslingam S., Ganesh S. 2006. Ranked set sampling versus simple random sampling in the estimation of the mean and the ratio. Journal of Statistics and Management Systems, 9(2), 459-472.
  • Al-Omari A.I., Jaber K., Al-Omari A. 2008. Modified ratio-type estimators of the mean using extreme ranked set sampling. Journal of Mathematics and Statistics, 4(3), 150-155.
  • Al-Omari A.I., Jemain A.A., Ibrahim K. 2009. New ratio estimators of the mean using simple random sampling and ranked set sampling methods. Investigación Operacional, 30(2), 97-108.
  • Kadılar C., Ünyazıcı Y., Çıngı H. 2009. Ratio estimator for the population mean using ranked set sampling. Statistical Papers, 50(2), 301-309.
  • Al-Omari A.I. 2012. Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling. Statistics and Probability Letters, 82(11), 1883-1890.
  • Singh H.P., Tailor R., Singh S. 2014. General procedure for estimating the population mean using ranked set sampling. Journal of Statistical Computation and Simulation, 84(5), 931-945.
  • Ozturk, O. 2018. Ratio estimators based on a ranked set sample in a finite population setting. Journal of the Korean Statistical Society, 47, 226-238.
  • Stokes L. S. 1977. Ranked set sampling with concomitant variables. Commun. Statist. Theor. Meth., A6(12), 1207-1211.
  • Bütün S. 2013. Keban Baraj Gölü’nde Yaşayan Alburnus Mossulensis Heckel, 1843’de Otolit Biyometrisi, Fırat Üniversitesi Fen Bilimleri Enstitüsü, Yüksek Lisans Tezi, Elazığ, 4-30.
There are 20 citations in total.

Details

Primary Language English
Journal Section Araştırma Makalesi
Authors

Sinem Şahin Tekin 0000-0003-3544-8123

Merve Kör This is me 0000-0001-5930-8489

Yaprak Özdemir 0000-0003-3752-9744

Publication Date December 25, 2020
Submission Date February 13, 2020
Acceptance Date September 26, 2020
Published in Issue Year 2020 Volume: 9 Issue: 4

Cite

IEEE S. Şahin Tekin, M. Kör, and Y. Özdemir, “A Theoretical Inference About Ratio Estimation of Population Mean Using Ranked Set Sampling Under Bivariate Normal Distribution”, Bitlis Eren Üniversitesi Fen Bilimleri Dergisi, vol. 9, no. 4, pp. 1469–1481, 2020, doi: 10.17798/bitlisfen.688795.

Bitlis Eren University
Journal of Science Editor
Bitlis Eren University Graduate Institute
Bes Minare Mah. Ahmet Eren Bulvari, Merkez Kampus, 13000 BITLIS