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The objective of the paper is to propose modified estimators for estimating the population mean by using the improved linear regression using auxiliary imformation with the coefficient of regression and coefficient of skewness of the auxiliary variables.

An Illustration           
We observe that the conditions discussed in the introduction for known coefficient of variation are satisfied for the data given in Walpoole, R. E., Myres, R. H., Myres, S. L., and Ye, K. (2005, page 473) dealing with measure of aerobic fitness is the oxygen consumption in volume per unit body weight per unit time. Thirty-one individuals were used in an experiment in order to be able to model oxygen consumption (y) against time to run one and half miles (x). consumption of required values has been done and we have the following.

       

For the population I and II we use the Data Sets data of Singh and Chaudhary (1986) page 177 and for the population III we use the data of Murthy (1967) page 228 in which fixed capital is denoted by X (auxiliary variable) and output of 80 factories are denoted by Y (study variable). For the population IV, the data is of cultivation and production of apple in district Baramulla of Kashmir (Jammu and Kashmir) in which the apple production (in tons) is denoted by Y (study variable) and number of apple trees are denoted by X (auxiliary variable, 1unit = 100 trees) in 117 villages of the Baramulla region of Jammu and Kashmir in 2010-2011 (Source: RC Mproject, pilot survey for estimation of cultivation andproduction of apple in district Baramulla, RC Mapproved project).

       

Table 1: Characteristics of these populations

       

 

Table 1: Percentage gain in efficiency of the proposed estimator  with respect to  and

 

CONCLUSION

The use of proposed estimator is limited for the situations when coefficient of variation is known. However, in case of unknown coefficient of variations its estimated value may be used after studying the performance of the estimator (robustness) against different values of CV, if the guess is in error say 5%, 10%, 15%. 20%, 25%, 50%. Further work is being done in this direction.

REFERENCES

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Panda, K. B., & Das, P. (2018). Efficient hierarchic predictive multivariate product estimator based on harmonic mean. International Journal of Mathematics Trends and Technoloy (IJMTT) – 56(6), pp. 14-18.

Gupta, Sat & Shabbir, Javid (2008). Variance estimation in simple random sampling using auxiliary information. Hacettepe Journal of Mathematics and Statistics, 37(1), 57-67.