Estimation of variance of the difference-cum-ratio-type exponential estimator in simple random sampling (original) (raw)
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In this paper, three difference-cum-ratio estimators for estimating finite population coefficient of variation of the study variable using known population mean, population variance and population coefficient of variation of auxiliary variable were suggested. The biases and mean square errors (MSEs) of the proposed estimators were obtained. The relative performance of the proposed estimators with respect to that of some existing estimators were assessed using two populations’ information. The results showed that the proposed estimators were more efficient than the usual unbiased, ratio type, exponential ratio-type, difference-type and other existing estimators considered in the study.
In many sampling situations, researchers come across variety of data. These data are largely affected by the parent distribution. There are characteristics which some data share based on the parent distribution. These characteristics define their distribution as well as their behavior. The use of auxiliary variable in estimating a study variable has been on the increase. Auxiliary variable has been used in estimating population means as well as variances. The variance is very sensitive to distribution. Thus, estimating the variance using auxiliary variable might lead to some unexpected results. Hence the need to check the effect of the distribution of the performances of some selected classes of variance estimators. Twelve estimators were selected for comparison. Eight distributions were considered using simulation study. The selected distributions are: Normal, Chi-square, Uniform, Gamma, Exponential, Poisson, Geometric and Binomial. A population size of 330 was used while sample size of 30 was considered using simple random sample without replacement. The estimators were compared using Bias, and Mean Square Error. The performances of the estimators vary in some distributions. The gamma and exponential distributions showed wide variability. The performances of the estimators based on Bias is the same as that based on Mean Square Error. The Mean Square Errors were ranked. The best estimator is t 1 followed be t 10 and t 12. The results showed that the estimators are not distribution free.
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In the present manuscript, we have proposed a new efficient class of estimators for the population variance of the study variable using information on the auxiliary variable. The expressions for bias and mean square error (MSE) of the proposed estimator are obtained up to the first order of approximation. An optimum estimator for the proposed estimator is also obtained and its optimum properties are studied. It is shown that the proposed estimator is more efficient than sample variance, traditional ratio estimator due to Isaki (1983), Singh et al. (2011) exponential ratio estimator, estimator based on Kadilar and Cingi (2003) ratio estimator for the population mean etc. estimators under optimum conditions. For illustration, an empirical study is also carried out.
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