A MODIFIED EXPONENTIAL-TYPE ESTIMATOR FOR POPULATION MEAN WITH TWO AUXILIARY VARIABLES IN TWO PHASE SAMPLING

Abstract

The ratio estimators of finite population mean are applicable in various fields such as health, education, agriculture etc. Because one of the parameters used by this field in decision making includes the mean and very efficient estimation of this parameter will improve the outcome of such decision. Ratio estimators are applicable when the population mean of auxiliary variable X is known. But in real life situation complete information about population mean are usually unavailable which make ratio estimator impracticable. However, the ratio estimator is always bias and sometimes less efficient. In other to improve the efficiency and reduce the biasedness of existing estimator, the proposed estimators were modified using exponential as one of the improvement strategies. The inability to apply estimators in real-life scenarios stems from a lack of understanding of the auxiliary variable's population mean. The effectiveness of a class of a finite population mean in a double sampling estimator is investigated when the population mean of an auxiliary variable is estimated using exponential-type based on a preliminary large sample. Taylor series expansion up to second degree approximation was used to obtain the suggested estimators' biases and mean square errors. The suggested estimators' efficiency was compared to that of some relevant current estimators in an empirical study using four (4) real life data sets. The suggested estimators have lower mean square errors and higher percentage relative efficiencies than related estimators investigated in the study, according to the results. In addition, the present research can be used in any area of estimation and study variable. The estimators modified in this research work can be used in sampling theory at the estimation stage.