Dual to Ratio cum Product Estimators of Finite Population Mean Using Auxiliary Attribute(s) in Stratified Random Sampling

The problem of estimating the population mean in un-stratified sampling strategies to estimate the finite the presence of an auxiliary variable has been widely discussed in finite population sampling literature [1], suggested a class of estimators of the population mean using one auxiliary variable in the stratified random sampling and examined the MSE of the estimators up to the kth order of approximation [2-8] suggested some ratio cum product estimators in simple random sampling [10, 11] suggested some exponential ratio type estimators. However in many practical situations instead of existence of auxiliary variables there exist some auxiliary attributes (say), which are highly correlated with the study variable y. Taking into consideration the point biserial correlation coefficient between auxiliary attribute and the study variable y, several authors including [12-17] envisaged large number of improved estimators for the population mean of the study variable y. There are some situations when in place of one auxiliary attribute, we have information on two qualitative variables. For illustration, to estimate the hourly wages we can use the information on marital status and region of residence [18]. Here we assume that both auxiliary attributes have significant point bi-serial correlation with the study variable and there is significant phi-correlation [19] between the two auxiliary attributes. Using point biserial correlation and phi-correlation [20-24] have proposed improved estimators for the population mean of the study variable y. often proved as useful in improving the precision of