Distribution Effect on the Efficiency of Some Classes of Population Variance Estimators Using Information of an Auxiliary Variable Under Simple Random Sampling (original) (raw)

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.

Modified Estimators of Population Variance in Presence of Auxiliary Information

2012

This paper proposes estimator of population variance using information on known parameters of auxiliary variable. The variances of the proposed estimators are obtained. It has been shown that using modified sampling fraction the proposed estimators are more efficient than the usual unbiased estimator of population variance and usual ratio estimator for population variance under certain given conditions. Empirical study is also carried out to demonstrate the merits of the proposed estimators of population variance over other estimators considered in this paper.

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.

Estimation of Population Variance Utilizing Auxiliary Information

In this article, an estimation procedure for the population variance utilizing auxiliary information and known coefficient of variation is proposed. The Bias and mean square error of proposed estimator are found up to first order of approximation. A comparative study with the usual unbiased estimator and usual ratio estimator for population variance has been made. Numerical study is also given at the end of the article to support the theoretical findings.

NEW EFFICIENT CLASS OF ESTIMATORS FOR THE POPULATION VARIANCE

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.

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.

A General Family of Estimators for Estimating Population Variance Using Known Value of Some Population Parameter(s)

A general family of estimators for estimating the population variance of the variable under study, which make use of known value of certain population parameter(s), is proposed. Some well known estimators have been shown as particular member of this family. It has been shown that the suggested estimator is better than the usual unbiased estimator, Isaki's (1983) ratio estimator, Upadhyaya and Singh's (1999) estimator and Kadilar and Cingi (2006). An empirical study is carried out to illustrate the performance of the constructed estimator over others.

Improved Estimator of Population Variance Using Measure of Dispersion of Auxiliary Variable

Oriental Journal of Physical Sciences, 2018

This research study is designed to obtain a more precise class of estimators of a population variance by taking advantage of relation between auxiliary variable and study variable. Here a class of new modified ratio type estimators of population variance by using coefficient of variation (CV), standard deviation, mean and median of auxiliary variable. Further empirical study is made to compare bias and mean square error (MSE) of proposed estimators with the existing estimators. Expressions for bias and MSE are obtained. Few secondary data sets are used to check the efficiency of proposed estimators of population variance.

Generalized Estimator of Population Variance utilizing Auxiliary Information in Simple Random Sampling Scheme

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.

A Family of Estimators of Population Variance Using Information on Auxiliary Attribute

This paper proposes some estimators for the population variance of the variable under study, which make use of information regarding the population proportion possessing certain attribute. Under simple random sampling without replacement (SRSWOR) scheme, the mean squared error (MSE) up to the first order of approximation is derived. The results have been illustrated numerically by taking some empirical population considered in the literature.