Modified Ratio Estimators for Population Mean Using Function of Quartiles of Auxiliary Variable

Abstract

The present paper deals with some new modified ratio estimators for estimation of population mean using the quartiles and its functions of the auxiliary variable. The bias and the mean squared error of the proposed estimators are obtained and are compared with some of the existing modified ratio estimators. As a result, we have observed that the proposed modified ratio estimators perform better than the existing modified ratio estimators. These are explained with the help of numerical examples. value of the population quartiles and their functions of the auxiliary variable to improve the ratio estimators. Further we know that the value of quartiles and their functions are unaffected and robustness by the extreme values or the presence of outliers in the population values unlike the other parameters like the mean, coefficient of variation, coefficient of skewness and coefficient of kurtosis etc. These points discussed above have motivated us to introduce a modified ratio estimator using the known value of the population quartiles and their functions of the auxiliary variable. There are three quartiles called, first quartile, second quartile and third quartile. The second quartile is equal to the median. The first quartile is also called lower quartile and is denoted by . The third quartile is also called upper quartile and is denoted by . The lower quartile is a point which has 25% observations less than it and 75% observations are above it. The upper quartile is a point with 75% observations less than it and 25% observations are above it. The inter-quartile range is another range used as a measure of the spread. The difference between upper and lower quartiles , which is called the inter-quartile range, also indicates the dispersion of a data set. The inter-quartile range spans 50% of a data set, and eliminates the influence of outliers because, in effect, the highest and lowest quarters are removed. The formula for inter-quartile range is: