A new improved class of ratio-product type exponential estimators of the population variance

FARAH NAZ, Tahir Nawaz, Muhammad Abid, Tianxiao Pang
2020 Scientia Iranica. International Journal of Science and Technology  
Several auxiliary information-based estimators of the population variance are available in the existing literature of survey sampling. Mostly, these estimators are based on conventional dispersion measures of the auxiliary variable. In this study, a generalized class of ratio-product type exponential estimators of the population variance is proposed which integrates the auxiliary information on non-conventional dispersion measures under simple random sampling in the ratio-type exponential class
more » ... of estimators. The performance of the proposed estimators is compared, theoretically and numerically, with the several existing estimators of the population variance. It is established that the proposed class of estimators outperforms the existing estimators in terms of the lower mean square and relative root mean square errors. Moreover, the percentage relative efficiency of the proposed estimators is much higher as compared to their counterparts. Keywords: auxiliary variable, mean square error, percentage relative efficiency, relative root mean square error, simple random sampling. (Nawaz, T.) 2 studies, statistical process monitoring in industry, medical and biological sciences, and many other related fields; see for example [1] [2] [3] [4] [5] [6] [7] . Along with population mean, the estimation of variance is of great interest to make certain policy decisions in many practical situations such as agriculture, business, stock investments, production planning in manufacturing industry, services industry, ecology, seismology, and medical sciences are few to mention [8] [9] [10] . Therefore, efficient estimation of the mean and variance are equally important for effective decision making. The estimation of variance in the context of ratio-type methods of estimation, using auxiliary information, has been considered by various researchers. Usually, conventional auxiliary measures such as mean, median, quartiles, variance, coefficient of kurtosis, variation, skewness, and the correlation between the study and auxiliary variables are employed under ratio and regression type estimation structures to improve the efficiency of the estimators of variance. For example, see [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] as well as their cited references for details on this subject. The auxiliary measures used in most of the existing ratio-type estimators of variance are non-resistant to the presence of outliers. The use of such measures can undermine the efficiency of the ratio-type estimators of variance if some outliers are present in the data. Thus, there is need for incorporation of some outlier resistant auxiliary measures to develop more stable ratiotype estimators.
doi:10.24200/sci.2020.53481.3260 fatcat:a4m4chvicbamnnfyb6n25wyt4y