Global Journal of Science Frontier Research, F: Mathematics and Decision Science, Volume 21 Issue 4

improved class of difference-type estimators for population median using two auxiliary variables under simple random scheme and two phase sampling scheme. So far, the shortcoming of the existing estimators is that, while some of these estimators are less biased with large mean square error (MSE), others are highly biased with less MSE. Based on these developments as a benchmark, this study proposes a separate ratio exponential-type estimator in simple random sampling and two phase sampling schemes with two auxiliary variables that will be more precise with greater gains in efficiency to estimate the median for finite population. a) Notations Consider a finite population = { 1 , 2 , … , } with size N. Let , ,and be the study and auxiliary variables respectively. Let represents the samples of the interest variable and and represents the samples of the auxiliary variablesknown for every unit in the population for the ℎ element drawn under SRSWOR. Let ( ) , ( ) , and ( ) represent the density functions of the random variables with � , � , and � being the samples from the population median , and respectively, with correlation coefficient = 4( 11 − 0.25) , where 11 = ( ≤ ∩ ≤ ) , = 4( 11 − 0.25) , where 11 = ( ≤ ∩ ≤ ) , and = 4( 11 − 0.25) , where 11 = ( ≤ ∩ ≤ ) , (considering the continuous distributions of all variables , , and with their marginal densities respectively as → ∞ ). For large sample approximations, the following are obtainable: � = (1 + 0 ) , � = (1 + 1 ) , � = (1 + 2 ) , 0 = � − 1 = � − 2 = � − ( 0 ) = ( 1 ) = ( 2 ) = 0 = 1− 4 ( 02 ) = 2 ( 12 ) = 2 ( 22 ) = 2 ( 0 1 ) = ( 0 2 ) = = { ( )} −1 = { ( )} −1 ℎ = { ℎ ( ℎ )} −1 1 = 2 = where, it is also assumed that the distribution function ( ) , ( ) , and ( ) are nonnegative. II. E xisting E stimators under S imple R andom S ampling This section considers some existing estimators in simple random sampling in estimating population median and the expression of bias and MSE up to the first order approximation as follows; Towards the Efficiency of the Ratio Estimator for Population Median in Survey Sampling © 2021 Global Journals 1 Global Journal of Science Frontier Research Volume XXI Issue IV Year 2021 38 ( F ) Version I N otes