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

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.

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 Using Auxiliary Information More Efficiently in Population Variance Estimation - A New Family of Estimators

2020 ◽  
Vol 2 (2) ◽  
pp. 1-12
Author(s):  
Kalim Ullah ◽  
Zawar Hussain ◽  
Salman Arif Cheema
Keyword(s):  
Finite Population ◽  
Variance Estimation ◽  
Theoretical Study ◽  
Mean Squared Error ◽  
Auxiliary Information ◽  
Auxiliary Variable ◽  
First Order ◽  
New Family ◽  
Squared Error ◽  
Estimation Of Variance

In this article, we have suggested estimation of variance in finite population by using known values of parameter related to auxiliary information such as rank and second raw moment of auxiliary variable in stratified random sampling. The expression for the bias and mean squared error (MSE) of the suggested estimator are obtained up to first order of approximation. The proposed estimator is efficient comparatively various other estimators. A numerical and theoretical study are performed to support the suggested estimator.

scholarly journals Estimation of Population Median under Robust Measures of an Auxiliary Variable

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Muhammad Irfan ◽  
Maria Javed ◽  
Sandile C. Shongwe ◽  
Muhammad Zohaib ◽  
Sajjad Haider Bhatti
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Real Life ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
First Order ◽  
Mathematical Properties ◽  
Squared Error ◽  
Class Of Estimators ◽  
Robust Measures

In this paper, a generalized class of estimators for the estimation of population median are proposed under simple random sampling without replacement (SRSWOR) through robust measures of the auxiliary variable. Three robust measures, decile mean, Hodges–Lehmann estimator, and trimean of an auxiliary variable, are used. Mathematical properties of the proposed estimators such as bias, mean squared error (MSE), and minimum MSE are derived up to first order of approximation. We considered various real-life datasets and a simulation study to check the potentiality of the proposed estimators over the competitors. Robustness is also examined through a real dataset. Based on the fascinating results, the researchers are encouraged to use the proposed estimators for population median under SRSWOR.

scholarly journals Thematic Maps for the Variation of Bearing Capacity of Soil Using SPTs and MATLAB

Geosciences ◽  
2020 ◽  
Vol 10 (9) ◽  
pp. 329
Author(s):  
Mahdi O. Karkush ◽  
Mahmood D. Ahmed ◽  
Ammar Abdul-Hassan Sheikha ◽  
Ayad Al-Rumaithi
Keyword(s):  
Bearing Capacity ◽  
Mean Squared Error ◽  
Ground Level ◽  
The Other ◽  
Thematic Maps ◽  
First Order ◽  
Squared Error ◽  
Order Polynomial ◽  
Interpolation Polynomials ◽  
Penetration Tests

The current study involves placing 135 boreholes drilled to a depth of 10 m below the existing ground level. Three standard penetration tests (SPT) are performed at depths of 1.5, 6, and 9.5 m for each borehole. To produce thematic maps with coordinates and depths for the bearing capacity variation of the soil, a numerical analysis was conducted using MATLAB software. Despite several-order interpolation polynomials being used to estimate the bearing capacity of soil, the first-order polynomial was the best among the other trials due to its simplicity and fast calculations. Additionally, the root mean squared error (RMSE) was almost the same for the all of the tried models. The results of the study can be summarized by the production of thematic maps showing the variation of the bearing capacity of the soil over the whole area of Al-Basrah city correlated with several depths. The bearing capacity of soil obtained from the suggested first-order polynomial matches well with those calculated from the results of SPTs with a deviation of ±30% at a 95% confidence interval.

A Class of Estimators of the Population Mean Using Multi­Auxiliary Information

1983 ◽  
Vol 32 (1-2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Srivastava ◽  
H. S. Jhajj
Keyword(s):  
Mean Squared Error ◽  
Broad Class ◽  
Auxiliary Variable ◽  
Population Parameters ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Squared Error ◽  
Class Of Estimators ◽  
The Mean ◽  
Asymptotic Mean Squared Error

For estimating the mean of a finite population, Srivastava and Jhajj (1981) defined a broad class of estimators which we information of the sample mean as well as the sample variance of an auxiliary variable. In this paper we extend this class of estimators to the case when such information on p(> 1) auxiliary variables is available. The estimators of the class involve unknown constants whose optimum values depend on unknown population parameters. When these population parameters are replaced by their consistent estimates, the resulting estimators are shown to have the same asymptotic mean squared error. An expression by which the mean squared error of such estimators is smaller than those which use only the population means of the auxiliary variables, is obtained.

scholarly journals Two- Phase Stratified Sampling Estimator for Population Mean in The Presence of Nonresponse Using Single Auxiliary Variable

2020 ◽  
Vol 8 (2) ◽  
pp. 49-56
Author(s):  
Akan Anieting
Keyword(s):  
Mean Squared Error ◽  
Auxiliary Variable ◽  
Stratified Sampling ◽  
Second Phase ◽  
Two Phase ◽  
Population Mean ◽  
Squared Error ◽  
Large Sample Approximation ◽  
Sample Approximation ◽  
Phase Sample

In this article, a new estimator for population mean in two-phase stratified sampling in the presence of nonresponse using single auxiliary variable has been proposed. The bias and Mean Squared Error (MSE) of the proposed estimator has been given using large sample approximation. The empirical study shows that the MSE of the proposed estimator is more efficient than existing estimators. The optimum values of first and second phase sample have been determined.

scholarly journals A Family of Difference-Cum-Exponential Type Estimators for Estimating the Population Variance Using Auxiliary Information in Sample Surveys

2014 ◽  
Vol 1 ◽  
pp. 15-21
Author(s):  
H.S. Jhajj ◽  
Kusam Lata
Keyword(s):  
Linear Regression ◽  
Exponential Type ◽  
Random Sampling ◽  
Sampling Design ◽  
Mean Squared Error ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Double Sampling ◽  
Population Variance ◽  
Squared Error

Using auxiliary information, a family of difference-cum-exponential type estimators for estimating the population variance of variable under study have been proposed under double sampling design. Expressions for bias, mean squared error and its minimum values have been obtained. The comparisons have been made with the regression-type estimator by using simple random sampling at both occasions in double sampling design. It has also been shown that better estimators can be obtained from the proposed family of estimators which are more efficient than the linear regression type estimator. Results have also been illustrated numerically as well asgraphically.

scholarly journals A generalized exponential-type estimator for population mean using auxiliary attributes

PLoS ONE ◽  
2021 ◽  
Vol 16 (5) ◽  
pp. e0246947
Author(s):  
Sohail Ahmad ◽  
Muhammad Arslan ◽  
Aamna Khan ◽  
Javid Shabbir
Keyword(s):  
Exponential Type ◽  
Random Sampling ◽  
Finite Population ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Stratified Random Sampling ◽  
Population Mean ◽  
First Order ◽  
Squared Error ◽  
Class Of Estimators

In this paper, we propose a generalized class of exponential type estimators for estimating the finite population mean using two auxiliary attributes under simple random sampling and stratified random sampling. The bias and mean squared error (MSE) of the proposed class of estimators are derived up to first order of approximation. Both empirical study and theoretical comparisons are discussed. Four populations are used to support the theoretical findings. It is observed that the proposed class of estimators perform better as compared to all other considered estimator in simple and stratified random sampling.

Sign in / Sign up

Export Citation Format

Share Document