Abstract
In this paper we have proposed a class of modified ratio type variance estimators for estimation of population variance of the study variable using Quartiles and their functions of the auxiliary variable are known. The biases and mean squared errors of the proposed estimators are obtained and also derived the conditions for which the proposed estimators perform better than the traditional ratio type variance estimator and existing modified ratio type variance estimators. Further we have compared the proposed estimators with that of traditional ratio type variance estimator and existing modified ratio type variance estimators for certain known populations. From the numerical study it is observed that the proposed estimators perform better than the traditional ratio type variance estimator and existing modified ratio type variance estimators.
Highlights
Consider a finite population U = {U1, U2, ... , UN } of N distinct and identifiable units
We consider the au xiliary informat ion to improve the efficiency of the estimation of population variance
For want of space; for the sake of convenience to the readers and for the ease of comparisons, the biases and mean squared errors of the existing modified rat io type variance estimators given in Table 1 are represented in single class as given below: B S K2Ci = γSy2 AKCi AKCi β2(x) − 1 − (λ22 − 1) ; i = 1,2,3 and 4 (7)
Summary
Isaki[10] suggested a ratio type variance estimator for the population variance Sy2 when the population variance Sx2 of the au xiliary variable X is known together with its bias and mean squared error and are as given below:. Suggested four ratio type variance estimators using known values of Co-efficient of variation CX and Co-efficient of Kurtosis β2(x) of an au xiliary variable X together with their biases and mean squared errors as given in the Table 1. Subraman i and Ku marapandiyan[21] used Quart iles and their functions of the au xiliary variab le like Inter-quartile range, Semi-quartile range and Semi-quartile average to improve the ratio estimators in estimation of population mean. The points discussed above have motivated us to introduce a modified ratio type variance estimators using the known values of the quartiles and their functions of the auxiliary variable. Mean squared error MMMMMM(. ) γ Sy4 β2(y) − 1 + AK2C 1 β2(x) − 1 − 2AKC 1(λ22 − 1) γ Sy4 β2(y) − 1 + AK2C 2 β2(x) − 1 − 2AKC 2(λ22 − 1) γ Sy4 β2(y) − 1 + AK2C 3 β2(x) − 1 − 2AKC 3(λ22 − 1) γ Sy4 β2(y) − 1 + AK2C 4 β2(x) − 1 − 2AKC 4(λ22 − 1)
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