On Bivariate Ranked Set Sampling for Ratio and Regression Estimators

Abstract Relative performance of bivariate ranked set sampling (BVRSS), with respect to ranked set sampling (RSS) and simple random sampling (SRS), for estimating the population mean using ratio and regression methods is investigated. Properties of the proposed estimators are derived. Simulation study is conducted to gain insight in the behaviour of the relative efficiency of BVRSS relative to other sampling scheme. Also, real data that consist of heights and diameters of 399 trees are used to illustrate the procedure. The result of the simulation study and the real data illustration indicate that using BVRSS for ratio and regression estimation is more efficient than using a SRS and an RSS in most of the cases.

[1]  Hani M. Samawi,et al.  Estimating the Population Mean Using Extreme Ranked Set Sampling , 1996 .

[2]  G. P. Patil,et al.  Ranked Set Sampling: a Bibliography , 2004, Environmental and Ecological Statistics.

[3]  M. S. Ridout,et al.  On ranked set sampling for multiple characteristics , 2003, Environmental and Ecological Statistics.

[4]  Ganapati P. Patil,et al.  Relative precision of ranked set sampling: A comparison with the regression estimator , 1993 .

[5]  G. McIntyre,et al.  A method for unbiased selective sampling, using ranked sets , 1952 .

[6]  Hani M. Samawi,et al.  Estimation of Ratio Using Rank Set Sampling , 1996 .

[7]  M. F. Al-Saleh,et al.  Double-ranked set sampling , 2000 .

[8]  Weighted Extreme Ranked Set Sample for Skewed Population , 2002 .

[9]  I. Olkin,et al.  Sampling theory of surveys, with applications , 1955 .

[10]  P. Yu,et al.  Regression estimator in ranked set sampling. , 1997, Biometrics.

[11]  Stephen L. Rathbun,et al.  The Population Dynamics of a Long-Lived Conifer (Pinus palustris) , 1988, The American Naturalist.

[12]  Amer Ibrahim Al-Omari,et al.  Multistage ranked set sampling , 2002 .

[13]  G. P. Patil,et al.  Ranked set sampling: an annotated bibliography , 1995, Environmental and Ecological Statistics.

[14]  Hani M. Samawi,et al.  On the Estimation of the Distribution Function Using Extreme and Median Ranked Set Sampling , 2001 .

[15]  Mohammad Fraiwan Al-Saleh,et al.  Theory & Methods: Estimation of bivariate characteristics using ranked set sampling , 2002 .

[16]  Waldo Emerson Nelson,et al.  Textbook of Pediatrics , 1969 .

[17]  Hani M. Samawi.  On double extreme rank set sample with application to regression estimator , 2002 .

[18]  Kazumasa Wakimoto,et al.  On unbiased estimates of the population mean based on the sample stratified by means of ordering , 1968 .