Hybrid class of robust type estimators for variance estimation using mean and variance of auxiliary variable

Abstract

This study is completed for the estimation of unknown population variance for the variable of mean and variance of interest. To accomplish this task, a new generalized class of robust kind of variance estimators proposed utilizing known descriptives of auxiliary variable, for example, Mid-range, Hodges-Lehmann Mean, Tri-mean, deciles mean, coefficient of skewness, interquartile range, first quartile, coefficient of kurtosis, semi-interquartile average, inter decile range and Mean, etc. These conventional measures of auxiliary variable improve the accuracy of the suggested class under simple random sampling without replacement (SRSWOR) scheme. The properties such as the bias, mean square errors (MSE), and least MSE of the suggested class are derived up to first order of approximation. The superiority conditions of the developed class of estimators over existing estimators are also made out theoretically. Finally, numerical representation is also completed for the motivations behind the article. The usual variance estimator is considered as a benchmark for comparing all considered estimators in numerical illustration. The results have been indicated that the suggested class is performing better than the usual variance estimator and all other thoughts about existing estimators.