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 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 Variance Estimator Using Tri-mean and Inter Quartile Range of Auxiliary Variable

2017 ◽  
Vol 1 ◽  
pp. 83-91
Author(s):  
S.K. Yadav ◽  
Sheela Misra ◽  
S.S. Mishra ◽  
Shankar Prasad Khanal
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Population Parameter ◽  
Variance Estimator ◽  
Population Variance ◽  
Inter Quartile Range ◽  
First Order ◽  
Squared Error ◽  
Quartile Range

Background: Whenever the population is large and it is very time taking and costly to take observation on each unit of the population then sampling is the only way to get the appropriate estimate of the population parameter under consideration. Many authors have given many estimators for estimating population variance with greater efficiency.Objective: The objective of the study is to search for more efficient estimator than the competing estimators of population variance of study variable.Materials and Methods: The estimator utilizing information on tri-mean and inter quartile range of auxiliary variable has been is developed. The expressions for the bias and mean squared error (MSE) of the proposed estimator have been derived up to the first order of approximation. A theoretical comparison of the proposed estimator has been made with the competing estimators of population variance.Results: The theoretical findings have been justified with the help of numerical example from some natural populations. It has been found that the proposed estimator is best among the competing estimators of population variance as it has least mean squared error among them.Conclusion: Since the proposed estimator is best among the competing estimator of the population variance, therefore it must be used for the improved estimation of population variance.Nepalese Journal of Statistics, 2017, Vol. 1, 83-91

Computation of Improved Searls Estimation of Population Variance Using Robust Auxiliary Parameters

2020 ◽  
Vol 13 ◽  
Author(s):  
S. K. Yadav ◽  
Dinesh Sharma ◽  
Julius Alade
Keyword(s):  
Mean Squared Error ◽  
Natural Populations ◽  
Auxiliary Variable ◽  
Efficient Estimation ◽  
Data Sets ◽  
Population Variance ◽  
Practical Applications ◽  
Squared Error ◽  
Natural Data ◽  
R Programming

Introduction: Variation is an inherent phenomenon whether in nature made things or man made. Thus, it looks important to estimate this variation. Various authors have worked in the direction of improved estimation of population variance utilizing the known auxiliary parameters for better policy making. Methods: In this article, a new searls ratio type class of estimator is suggested for elevated estimation of population variance of main variable. As the suggested estimator is biased, so its bias and mean squared error (MSE) have been derived up to the approximation of order-one. The optimum values for the Searls characterizing scalars are obtained. The minimum MSE of the introduced estimator is obtained for the optimum Searls characterizing scalars. A theoretical comparison between suggested estimator and the competing estimators has been made through their mean squared errors. The efficiency conditions of suggested estimator over competing estimators are also obtained. These theoretical conditions are verified using some natural data sets. The computation of R codes for the biases and MSEs of the suggested and competing estimators are developed and are used for three natural populations in Naz et al. (2019). The estimator with least MSE is recommended for practical utility. The empirical study has been done using R programming. Results: The MSEs of different competing and the suggested estimators are obtained for three natural populations. The estimator under comparison with the least MSE is recommended for practical applications. Discussion: The aim to search for the most efficient estimation for improved estimation, is fulfilled through the proper use of the auxiliary parameters obtained from the known auxiliary variable. The suggested estimator may be used for elevated estimation of population variance. Conclusion: The introduced estimator is having least MSE as compared to competing estimators of popularion variance for all three natural populations. Thus it may be recommended for the application in various fields.

scholarly journals Modified ratio estimators of population mean using linear combination of co-efficient of skewness and quartile deviation

2013 ◽  
Vol 31 (1) ◽  
pp. 39 ◽  
Author(s):  
M. Iqbal Jeelani ◽  
S. Maqbool
Keyword(s):  
Linear Combination ◽  
Auxiliary Variable ◽  
Degree Of Approximation ◽  
Linear Combinations ◽  
Study Variable ◽  
Population Mean ◽  
Mean Squared Errors ◽  
Ratio Estimators ◽  
Coefficient Of Skewness ◽  
Better Than

The present paper deals with the estimation of population mean of the study variable using the linear combination of known population values of coefficient of skewness and quartile deviation of auxiliary variable. Two modified ratio estimators for estimation of population mean of the study variable involving the above linear combinations are being used. Mean squared errors and biases up to the first degree of approximation are derived and compared with the proposed modified ratio estimators. The proposed modified ratio estimators perform better than the existing ratio estimators. The empirical study has been carried out in support of the results.

scholarly journals Almost Unbiased Ratio cum Product Estimator for Finite Population Mean with Known Median in Simple Random Sampling

2017 ◽  
Vol 1 ◽  
pp. 1-14
Author(s):  
Subramani Jambulingam ◽  
Ajith S. Master
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Numerical Study ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Study Variable ◽  
Population Mean ◽  
Squared Error ◽  
Product Estimator ◽  
Almost Unbiased

Introduction: In sampling theory, different procedures are used to obtain the efficient estimator of the population mean. The commonly used method is to obtain the estimator of the population mean is simple random sampling without replacement when there is no auxiliary variable is available. There are methods that use auxiliary information of the study characteristics. If the auxiliary variable is correlated with study variable, number of estimators are widely available in the literature.Objective: This study deals with a new ratio cum product estimator is developed for the estimation of population mean of the study variable with the known median of the auxiliary variable in simple random sampling.Materials and Methods: The bias and mean squared error of proposed estimator are derived and compared with that of the existing estimators by analytically and numerically.Results: The proposed estimator is less biased and mean squared error is less than that of the existing estimators and from the numerical study, under some known natural populations, the bias of proposed estimator is approximately zero and the mean squared error ranged from 6.83 to 66429.21 and percentage relative efficiencies ranged from 103.65 to 2858.75.Conclusion: The proposed estimator under optimum conditions is almost unbiased and performs better than all other existing estimators.Nepalese Journal of Statistics, 2017, Vol. 1, 1-14

scholarly journals GENERALISED EXPONENTIAL RATIO-TYPE ESTIMATOR FOR FINITE POPULATION VARIANCE UNDER RANDOM NON-RESPONSE

2021 ◽  
Vol 9 (01) ◽  
pp. 589-596
Author(s):  
Alisha Mittal ◽  
◽  
Manoj Kumar ◽  
Keyword(s):  
Unbiased Estimator ◽  
Finite Population ◽  
Research Paper ◽  
Auxiliary Variable ◽  
Population Variance ◽  
Study Variable ◽  
Numerical Illustration ◽  
The Family ◽  
Better Than

In this research paper an effort has been made for the estimation of population variance of the study variable by using information on certain known parameters of the auxiliary variable under non-response for scheme I and II given by Singh and Joarder (1998). Generalized exponential ratio-type estimator has been proposed and their properties have been studied under non response techniques and conditions were found when the family of proposed estimators identified by using different choices for (P, Q) performed better than the usual unbiased estimator. It was also observed that for different values of α ∈ (0.0, 1.0), the estimators and were found to be best under numerical illustration.

scholarly journals Efficient transformed ratio-type estimator using single auxiliary information

2021 ◽  
Vol 48 (2) ◽  
Author(s):  
Sana Amjad ◽  
◽  
Muhammad Ismail ◽  
Keyword(s):  
Mean Squared Error ◽  
Order Approximation ◽  
Real Life ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Variance Estimators ◽  
Life Data ◽  
Squared Error ◽  
Real Life Data ◽  
Better Than

This paper provides an efficient transformed ratio-type estimator to estimate the study variable's population variance by utilizing information of a single auxiliary variable under simple random sampling without replacement. The bias and mean squared error of the proposed estimator are derived up-to 1st order approximation. In addition to this, the efficiency comparison of the proposed estimator has been done with traditional ratio-type variance estimator and some other widely used modified ratio-type variance estimators by taking real-life data. A simulation study has also been carried out to see the performance of the proposed estimator. It is worth noticing that our proposed estimator performs better than the competing estimators in real-life data applications as the mean squared error and root mean squared error of our proposed estimator are smaller than the competing estimators. Hence, our proposed estimator is better than existing variance estimators.

scholarly journals Efficient Method of Estimating the Finite Population Mean Based on Two Auxiliary Variables in the Presence of Non-Response Under Stratified Sampling

2021 ◽  
Author(s):  
Housila P. Singh ◽  
Pragati Nigam
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Variables ◽  
Optimum Conditions ◽  
Study Variable ◽  
Numerical Illustration ◽  
Population Mean ◽  
Minimum Mean Squared Error ◽  
Squared Error ◽  
Class Of Estimators ◽  
Better Than

This article addresses the problem of estimating the population mean using information on two auxiliary variables in presence of non-response on study variable only under stratified random sampling. A class of estimators has been defined. We have derived the bias and mean squared error up to first order of approximation. Optimum conditions are obtained in which the suggested class of estimators has minimum mean squared error. In addition to Chaudhury et al. (2009) estimator, many estimators can be identified as a member of the suggested class of estimators. It has been shown that the suggested class of estimators is better than the Chaudhury et al. (2009) estimator and other estimators. Results of the present study are supported through numerical illustration.

scholarly journals Difference-Cum-Ratio Estimators for Estimating Finite Population Coefficient of Variation in Simple Random Sampling

2021 ◽  
pp. 13-29
Author(s):  
A. Audu ◽  
M. A. Yunusa ◽  
O. O. Ishaq ◽  
M. K. Lawal ◽  
A. Rashida ◽  
...  
Keyword(s):  
Coefficient Of Variation ◽  
Finite Population ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Population Variance ◽  
Study Variable ◽  
Difference Type ◽  
Ratio Estimators ◽  
Mean Square Errors ◽  
Two Populations

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.

scholarly journals Enhanced Mean Ratio Estimators of Auxiliary Variables Based on the Linear Mixture of Variances

2019 ◽  
pp. 1-16
Author(s):  
Damisa A. Saddam ◽  
Jamila Abdullahi ◽  
Umar Nura
Keyword(s):  
Mean Square Error ◽  
Coefficient Of Variation ◽  
Population Data ◽  
Auxiliary Variable ◽  
Mean Square ◽  
Auxiliary Variables ◽  
Population Variance ◽  
Constant Bias ◽  
Ratio Estimators ◽  
Better Than

This paper incorporates the variance of auxiliary variables to propose three improved ratio estimators of population mean. To enhance the efficiency of the proposed ratio estimators, a linear combination of the population coefficient of variation, kurtosis, skewness and the population variance of the auxiliary variable is harnessed. The properties relating to the suggested estimators are assessed using constant, bias and mean square error. We also provided practical study for illustration and corroboration using a population data consisting of the fixed capital, which is the supporting variable and output of 80 factories which are the study variables. The suggested improved ratio estimators performed better than other ratio estimators in the literature when compared using bias and mean square error.

Sign in / Sign up

Export Citation Format

Share Document