Modified Estimator of Finite Population Variance in Simple Random Sampling ARTICLE INFORMATION ABSTRACT (original) (raw)
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Modified Estimator of Finite Population Variance in Simple Random Sampling
NIPES Journal of Science and Technology Research, 2019
This paper deals with modification of Milton's estimator of population variance using coefficient of quartile deviation and unknown weight of auxiliary variable. The Bias and Mean Square Error (MSE) of proposed estimator are obtained up to the first order of approximation by Taylor's Series Method. The expression for the unknown weight is obtained and an empirical study was conducted to assess the performance of proposed estimator over some selected existing estimators. A numerical study is carried out to assess the efficiency of proposed estimator over the existing estimator with the aid of some known natural populations. Numerical study results shown that the proposed estimator performs better than the existing estimators.
Improved Estimator of Finite Population Variance Using Coefficient of Quartile Deviation
Asian Journal of Advanced Research and Reports, 2018
This study introduces a new, better, class of ratio estimators for the estimation of population variance of the study variable by using the coefficient of quartile deviation of auxiliary variable. Bias and mean square error of the proposed class of estimators are also derived. The conditions of efficiency comparison are also obtained. Simulation and different secondary data sets are used to evaluate the efficiency of proposed class of variance estimators over existing class of estimators. The empirical study shows that the suggested class of estimators is more efficient the existing class of estimators for the population variance.
Journal of Probability and Statistical Science, 2023
In this study, using the Simple Random Sampling without Replacement (SRSWOR) method, we propose a generalized estimator of population variance of the primary variable. Up to the first order of approximation, the bias and Mean Squared Error (MSE) expressions for the suggested estimator are produced. The suggested estimator's characterizing scalar is optimized, and for this optimal value of the characterizing constant, the suggested estimator's least MSE is also determined. The efficiency criteria of the suggested estimator over the other estimators are determined after a theoretical comparison of the proposed estimator with the other population variance estimators that already exist. Several actual natural populations are used to validate these efficiency parameters. For practical use in various application domains, the estimator with the lowest MSE and the best Percentage Relative Efficiency (PRE) is advised.
This paper suggests the generalized class of estimators, motivated by Sharma and Singh (2015), of finite population variance utilizing the known value of parameters related to an auxiliary variable such as quartile and its properties are studied in simple random sampling without replacement. The efficiency of proposed class of estimators is compared with some existing estimators discussed in literature and found that proposed generalized class of estimators is better than other existing estimators including usual unbiased estimator, estimators due to Isaki (1983), Das and Tripathi (1978) and estimators recently proposed by Singh and Pal (2016). An empirical as well as theoretical comparison is carried out to judge the performance of proposed class of estimators over other existing estimators of population variance using natural data set. MSC: 62D05 RESUMEN En este paper se sugiere una clase generalizada de estimadores motivada por los resultados de Sharma and Singh (2015), la varian...
Improved Estimation of Finite Population Variance Using Auxiliary Information
Communications in Statistics - Theory and Methods, 2013
We have addressed the problem of estimation of finite population variance using known values of quartiles of an auxiliary variable. Some ratio type estimators have been proposed with their properties in simple random sampling. The suggested estimators have been compared with the usual unbiased and ratio estimators. In addition, an empirical study is also provided in support of theoretical findings.
Improved Family of Estimators of Population Variance in Simple Random Sampling
Journal of Statistical Theory and Practice, 2013
In this article, we suggest a general procedure for estimating the population variance through a class of estimators. The bias and mean square error (MSE) of the proposed class of estimators are obtained to the first degree of approximation. The proposed class of estimators is more efficient than many other estimators, such as the usual variance estimator, ratio estimator, the Bahal and Tuteja (1991) exponential estimator, the traditional regression estimator, the Rao (1991) estimator, the Upadhyaya and Singh (1999) estimator, and the estimators. Four data sets are used for numerical comparison.
Improved Estimation of Population Variance Utilizing Known Auxiliary Parameters
Scholars Journal of Physics, Mathematics and Statistics
Even similar things, whether created artificially or naturally, can vary. We should therefore try to estimate this variation. For improved population variance estimate, we propose a Searls ratio type estimator in the current research employing data on the tri-mean and the third quartile of the auxiliary variable. Up to the first-degree approximation, the suggested estimator's bias and mean squared error (MSE) are determined. The characterising scalar's ideal value is discovered, and given this ideal value, the least MSE is discovered. The mean squared errors of the suggested estimator and the competing estimators are contrasted conceptually and experimentally. Given that it has the lowest MSE of the above competing estimators, the recommended estimator has been shown to be the most effective.
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.
An improved generalized class of estimators for population variance using auxiliary variables
Cogent Mathematics & Statistics, 2018
This paper proposed an improved generalized class of estimator for estimating population variance using auxiliary variables based on simple random sampling without replacement. The expression of mean square error of the proposed estimator is obtained up to the first order of approximation. We have derived the conditions for the parameters under which the proposed estimator performs better compared to the usual estimator and other existing estimators. An empirical study and simulation study are also carried out with the support of theoretical results.
Journal of Statistics Applications & Probability, 2013
In this paper we have suggested aratio type estimator for the estimation of population variance of the study variable using quartiles and its functions as an auxiliary variable. The expression of bias and mean squared error of the proposed estimator is derived up to first order approximation.The proposed estimator is compared with the other existing estimators and its efficiency condition is carried out. An empirical study is carried out with the help of four natural populations to judge the merits of the suggested estimator over other existing estimators practically.