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Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling

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  • Al-Omari, Amer Ibrahim

Abstract

In this article, two modified ratio estimators of the population mean are suggested provided that the first or third quartiles of the auxiliary variable can be established when the mean of the auxiliary variable is known. The double-sampling method is used to estimate the mean of the auxiliary variable if it is unknown. The suggested estimators are investigated under simple random sampling (SRS) and median ranked set sampling (MRSS) schemes. The new estimators when using MRSS are compared to their counterparts under SRS. The bias and the mean square error of the proposed estimators are derived. It turns out that the estimators are approximately unbiased and the MRSS estimators are more efficient than the SRS estimators, on the basis of the same sample size, correlation coefficient, and quartile. A real data set is used for illustration.

Suggested Citation

  • Al-Omari, Amer Ibrahim, 2012. "Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1883-1890.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1883-1890
    DOI: 10.1016/j.spl.2012.07.001
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    1. M. Al-Saleh & H. Samawi, 2007. "A note on inclusion probability in ranked set sampling and some of its variations," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 16(1), pages 198-209, May.
    2. N. Balakrishnan & T. Li, 2006. "Confidence Intervals for Quantiles and Tolerance Intervals Based on Ordered Ranked Set Samples," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 58(4), pages 757-777, December.
    3. Ozturk, Omer, 2007. "Two-sample median test for order restricted randomized designs," Statistics & Probability Letters, Elsevier, vol. 77(2), pages 131-141, January.
    4. Mohammad Al-Saleh & Ahmad Al-Ananbeh, 2007. "Estimation of the means of the bivariate normal using moving extreme ranked set sampling with concomitant variable," Statistical Papers, Springer, vol. 48(2), pages 179-195, April.
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