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

2018 ◽  
Vol 3 (1) ◽  
pp. 33-39
Author(s):  
Muhammad Khalil ◽  
Muhammad Ali ◽  
Usman Shahzad ◽  
Muhammad Hanif ◽  
Nasir Jamal
Keyword(s):  
Standard Deviation ◽  
Empirical Study ◽  
Research Study ◽  
Secondary Data ◽  
Auxiliary Variable ◽  
Data Sets ◽  
Mean Square ◽  
Population Variance ◽  
Study Variable ◽  
Class Of Estimators

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.

scholarly journals Improved Estimator of Finite Population Variance Using Coefficient of Quartile Deviation

2018 ◽  
pp. 1-6
Author(s):  
Komal Javed ◽  
Nasir Jamal ◽  
Muhammad Hanif ◽  
Muhammad Ali ◽  
Usman Shahzad ◽  
...  
Keyword(s):  
Finite Population ◽  
Secondary Data ◽  
Auxiliary Variable ◽  
Data Sets ◽  
Population Variance ◽  
Study Variable ◽  
Variance Estimators ◽  
Class Of Estimators ◽  
Efficiency Comparison ◽  
Variable Bias

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.

scholarly journals An Improved Ratio-Type Variance Estimator by Using Linear Combination of Diferent Measures of Location

2018 ◽  
Vol 3 (1) ◽  
pp. 24-32
Author(s):  
Muhammad Ali ◽  
Muhammad Khalil ◽  
Muhammad Hanif ◽  
Nasir Jamal ◽  
Usman Shahzad
Keyword(s):  
Research Study ◽  
Mean Squared Error ◽  
Auxiliary Variable ◽  
The Other ◽  
Primary Data ◽  
Data Sets ◽  
Variance Estimator ◽  
Population Variance ◽  
Study Variable ◽  
Squared Error

In this research study, modified family of estimators is proposed to estimate the population variance of the study variable when the population variance, quartiles, median and the coefficient of correlation of auxiliary variable are known. The expression of bias and mean squared error (MSE) of the proposed estimator are derived. Comparisons of the proposed estimator with the other existing are conducted estimators. The results obtained were illustrated numerically by using primary data sets. Theoretical and numerical justification of the proposed estimator was done to show its dominance.

scholarly journals Restructured class of estimators for population mean using an auxiliary variable under simple random sampling scheme

2020 ◽  
Vol 16 (1) ◽  
pp. 61-75
Author(s):  
S. Baghel ◽  
S. K. Yadav
Keyword(s):  
Random Sampling ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Sampling Scheme ◽  
Order Of Approximation ◽  
Study Variable ◽  
Population Mean ◽  
First Order ◽  
New Class ◽  
Class Of Estimators

AbstractThe present paper provides a remedy for improved estimation of population mean of a study variable, using the information related to an auxiliary variable in the situations under Simple Random Sampling Scheme. We suggest a new class of estimators of population mean and the Bias and MSE of the class are derived upto the first order of approximation. The least value of the MSE for the suggested class of estimators is also obtained for the optimum value of the characterizing scaler. The MSE has also been compared with the considered existing competing estimators both theoretically and empirically. The theoretical conditions for the increased efficiency of the proposed class, compared to the competing estimators, is verified using a natural population.

scholarly journals Some Median Type Estimators to Estimate the Finite Population Mean

2020 ◽  
pp. 48-58
Author(s):  
Waqar Hafeez ◽  
Javid Shabbir ◽  
Muhammad Taqi Shah ◽  
Shakeel Ahmed
Keyword(s):  
Linear Regression ◽  
Finite Population ◽  
Auxiliary Variable ◽  
Maximum Efficiency ◽  
Order Of Approximation ◽  
Study Variable ◽  
Sample Mean ◽  
First Order ◽  
Regression Estimators ◽  
Class Of Estimators

Researchers always appreciates estimators of finite population quantities, especially mean, with maximum efficiency for reaching to valid statistical inference.  Apart from ratio, product and regression estimators, exponential estimators are widely considered by survey statisticians. Motivated from the idea of exponential type estimators, in this article, we propose some new estimators utilizing known median of the study variable with mean of auxiliary variable. Theoretical properties of the suggested estimators are studied up to first order of approximation. In addition, an empirical and simulation study the comparison of median based proposed class of estimators with sample mean, ratio and linear regression estimators  are discussed. The results expose that the proposed estimators are more efficient than the existing estimators.

scholarly journals A Class of Modified Ratio Estimators for Estimation of Population Variance

2015 ◽  
Vol 11 (1) ◽  
pp. 91-114 ◽  
Author(s):  
J. Subramani ◽  
G. Kumarapandiyan
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Variance Estimator ◽  
Population Variance ◽  
Study Variable ◽  
Variance Estimators ◽  
Squared Error ◽  
Ratio Estimators ◽  
Better Than

Abstract In this paper we have proposed a class of modified ratio type variance estimators for estimation of population variance of the study variable using the known parameters of the auxiliary variable. The bias and mean squared error of the proposed estimators are obtained and also derived the conditions for which the proposed estimators perform better than the traditional ratio type variance estimator and existing modified ratio type variance estimators. Further we have compared the proposed estimators with that of the traditional ratio type variance estimator and existing modified ratio type variance estimators for certain natural populations.

scholarly journals A Note on Generalized Exponential Type Estimator for Population Variance in Survey Sampling

2015 ◽  
Vol 38 (2) ◽  
pp. 385-397 ◽  
Author(s):  
Javid Shabbir ◽  
Sat Gupta
Keyword(s):  
Exponential Type ◽  
Auxiliary Variable ◽  
Survey Sampling ◽  
Data Sets ◽  
Numerical Comparison ◽  
Order Of Approximation ◽  
Population Variance ◽  
First Order ◽  
Better Than

<p>Recently a new generalized estimator for population variance using information on the auxiliary variable has been introduced by Asghar, Sanaullah &amp; Hanif (2014). In that paper there was some inaccuracy in the bias and MSE expressions. In this paper, we provide the correct expressions for bias and MSE of the Asghar et al. (2014) estimator, up to the first order of approximation. We also propose a new generalized exponential type estimator for population variance which performs better than the existing estimators. Four data sets are used for numerical comparison of efficiencies.</p>

scholarly journals Efficiency of Ratio, Product, and Regression Estimators under Maximum and Minimum Values, Using Two Auxiliary Variables

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Abdullah Y. Al-Hossain ◽  
Mursala Khan
Keyword(s):  
Real Data ◽  
Data Sets ◽  
Mean Square ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
First Order ◽  
Regression Estimators ◽  
Class Of Estimators ◽  
Mean Square Errors ◽  
Better Than

To obtain the best estimates of the unknown population parameters have been the key theme of the statisticians. In the present paper we have suggested some estimators which estimate the population parameters efficiently. In short we propose a ratio, product, and regression estimators using two auxiliary variables, when there are some maximum and minimum values of the study and auxiliary variables, respectively. The properties of the proposed strategies in terms of mean square errors (variances) are derived up to first order of approximation. Also the performance of the proposed estimators have shown theoretically and these theoretical conditions are verified numerically by taking four real data sets under which the proposed class of estimators performed better than the other previous works.

scholarly journals Enhanced Estimators of Population Variance with the Use of Supplementary Information in Survey Sampling

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Showkat Ahmad Lone ◽  
Mir Subzar ◽  
Ankita Sharma
Keyword(s):  
Finite Population ◽  
Auxiliary Variable ◽  
Supplementary Information ◽  
Ratio Estimator ◽  
Population Variance ◽  
Measures Of Dispersion ◽  
Class Of Estimators ◽  
Efficiency Comparison ◽  
Improved Estimators ◽  
Theoretical Results

In the present study, we propose the proficient class of estimators of the finite population mean, while incorporating the nonconventional location and nonconventional measures of dispersion with coefficient of variation of the auxiliary variable. Properties associated with the suggested class of improved estimators are derived, and an efficiency comparison with the usual unbiased ratio estimator and other existing estimators under consideration in the present study is established. An empirical study has also been provided to validate the theoretical results. Finally, it is established that the proposed class of estimators of the finite population variance proves to be more efficient than the existing estimators mentioned in this study.

scholarly journals Enhancing the Mean Ratio Estimators for Estimating Population Mean Using Non-Conventional Location Parameters

2016 ◽  
Vol 39 (1) ◽  
pp. 63-79 ◽  
Author(s):  
Muhammad Abid ◽  
Nasir Abbas ◽  
Hafiz Zafar Nazir ◽  
Zhengyan Lin
Keyword(s):  
Empirical Study ◽  
Coefficient Of Variation ◽  
Auxiliary Variable ◽  
Mean Square ◽  
Linear Combinations ◽  
Population Correlation ◽  
Location Parameters ◽  
The Mean ◽  
Ratio Estimators ◽  
Mean Square Errors

<p>Conventional measures of location are commonly used to develop ratio estimators. However, in this article, we attempt to use some non-conventional location measures. We have incorporated tri-mean, Hodges-Lehmann, and mid-range of the auxiliary variable for this purpose. To enhance the efficiency of the proposed mean ratio estimators, population correlation coefficient, coefficient of variation and the linear combinations of auxiliary variable have also been exploited. The properties associated with the proposed estimators are evaluated through bias and mean square errors. We also provide an empirical study for illustration and verification.</p>

scholarly journals Adapted Exponential Type Estimator in the Presence of Non-response

2021 ◽  
Author(s):  
Ceren Ünal ◽  
Cem Kadilar
Keyword(s):  
Empirical Study ◽  
Exponential Type ◽  
Unbiased Estimator ◽  
Data Sets ◽  
Regression Estimator ◽  
Mean Square ◽  
Order Of Approximation ◽  
Auxiliary Variables ◽  
First Order ◽  
Theoretical Results

In this article, we propose an estimator using the exponential function for the population mean in the case of non-response on both the study and the auxiliary variables. The equations for the Bias and Mean Square Error (MSE) are derived to the first order of approximation and theoretical comparisons are made with existing estimators in literature. Besides, we examine the efficiency of the proposed estimator according to the classical ratio and regression estimator, Hansen-Hurwitz unbiased estimator, and the estimator of Singh et al. (2009). Following theoretical comparisons, we infer that the proposed estimator is more efficient than compared estimators under the obtained conditions in theory. Moreover, these theoretical results are supported numerically by providing an empirical study on five different data sets.

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