Some Improved Ratio Estimators Using Known Values of Some Population Parameters

Abstract

Abstract
In this study, three modified ratio estimators were proposed which were compared with some existing ratio estimators
depending on the value of  being considered. The conditions attached to these proposed modified ratio estimators are that:
1 0    , 1 ) (  
X
X xy
, 1 ) (  
X
c X x
and 1 ) (  
X
X xy
while those of the existing ones are: 1 ) ( 
 xy X
X

,
1 ) ( 
 xc X
X and
1 ) ( 
 xy X
X

which are in opposite direction to the proposed modified ratio estimators. Two data
sets ( populations I and II) are used to justify this work using their derived mean square error (mse) and the proposed
modified ratio estimators 1 raa y , 2 raa y and 3 raa y were found to be better and more efficient than those existing ratio
estimators. However, for populations I and II, 2 raa y and 3 raa y are preferred respectively because they had the least mean
square error (mse). In this study, whenever Y X , the range values of  was found to be wider (i.e. 6.0 1.0    ) than
when Y X ( i.e. 2.0 1.0    ). Hence, these proposed modified ratio estimators are recommended for future usage in
sample surveys.