scholarly journals On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling

2020 ◽  
Vol 2020 ◽  
pp. 1-13 ◽  
Author(s):  
Saddam Hussain ◽  
Mi Zichuan ◽  
Sardar Hussain ◽  
Anum Iftikhar ◽  
Muhammad Asif ◽  
...  
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Population Distribution ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Distribution Functions ◽  
Supplementary Information ◽  
Auxiliary Variables ◽  
Estimation Of Distribution

In this paper, we proposed two new families of estimators using the supplementary information on the auxiliary variable and exponential function for the population distribution functions in case of nonresponse under simple random sampling. The estimations are done in two nonresponse scenarios. These are nonresponse on study variable and nonresponse on both study and auxiliary variables. As we have highlighted above that two new families of estimators are proposed, in the first family, the mean was used, while in the second family, ranks were used as auxiliary variables. Expression of biases and mean squared error of the proposed and existing estimators are obtained up to the first order of approximation. The performances of the proposed and existing estimators are compared theoretically. On these theoretical comparisons, we demonstrate that the proposed families of estimators are better in performance than the existing estimators available in the literature, under the obtained conditions. Furthermore, these theoretical findings are braced numerically by an empirical study offering the proposed relative efficiencies of the proposed families of estimators.

scholarly journals Estimation of finite population distribution function with dual use of auxiliary information under non-response

PLoS ONE ◽  
2020 ◽  
Vol 15 (12) ◽  
pp. e0243584
Author(s):  
Sardar Hussain ◽  
Sohaib Ahmad ◽  
Sohail Akhtar ◽  
Amara Javed ◽  
Uzma Yasmeen
Keyword(s):  
Distribution Function ◽  
Finite Population ◽  
Population Distribution ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Distribution Functions ◽  
Auxiliary Variables ◽  
Sample Mean ◽  
Sample Distribution

In this paper, we propose two new families of estimators for estimating the finite population distribution function in the presence of non-response under simple random sampling. The proposed estimators require information on the sample distribution functions of the study and auxiliary variables, and additional information on either sample mean or ranks of the auxiliary variable. We considered two situations of non-response (i) non-response on both study and auxiliary variables, (ii) non-response occurs only on the study variable. The performance of the proposed estimators are compared with the existing estimators available in the literature, both theoretically and numerically. It is also observed that proposed estimators are more precise than the adapted distribution function estimators in terms of the percentage relative efficiency.

scholarly journals Finite Population Distribution Function Estimation Using Auxiliary Information Under Simple Random Sampling

2021 ◽  
Vol 3 (1) ◽  
pp. 29-38
Author(s):  
Sohaib Ahmad ◽  
Sardar Hussain ◽  
Sohail Ahmad
Keyword(s):  
Distribution Function ◽  
Random Sampling ◽  
Finite Population ◽  
Population Distribution ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Supplementary Information ◽  
Function Estimation ◽  
Distribution Function Estimation

In this paper, a new estimator for estimating the finite population distribution function(DF) are propose using supplementary information on the DF of the auxiliary variable under simple random sampling. A comparative study is conducted to compare, theoretically and numerically, the adapted distribution function estimators of Cochran (1940), Murthy (1967), Bahl and Tuteja (1991), Rao (1991), Singh et al. (2009) and Grover and Kaur (2014) with the proposed estimators. It is found that the proposed estimators always perform better than the adapted estimators in terms of MSE and percentage relative efficiency.

Ratio-Type Estimation Using Scrabled Auxiliary Variables in Stratification Under Simple Random Sampling and Ranked Set Sampling

2022 ◽  
pp. 62-85
Author(s):  
Carlos N. Bouza-Herrera ◽  
Jose M. Sautto ◽  
Khalid Ul Islam Rather
Keyword(s):  
Random Sampling ◽  
Mean Squared Error ◽  
Simple Random Sampling ◽  
Ranked Set Sampling ◽  
Auxiliary Variables ◽  
Mild Conditions ◽  
Squared Error ◽  
The Mean ◽  
Better Than

This chapter introduced basic elements on stratified simple random sampling (SSRS) on ranked set sampling (RSS). The chapter extends Singh et al. results to sampling a stratified population. The mean squared error (MSE) is derived. SRS is used independently for selecting the samples from the strata. The chapter extends Singh et al. results under the RSS design. They are used for developing the estimation in a stratified population. RSS is used for drawing the samples independently from the strata. The bias and mean squared error (MSE) of the developed estimators are derived. A comparison between the biases and MSEs obtained for the sampling designs SRS and RSS is made. Under mild conditions the comparisons sustained that each RSS model is better than its SRS alternative.

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 Estimation of finite population mean using dual auxiliary variable for non-response using simple random sampling

2021 ◽  
Vol 7 (3) ◽  
pp. 4592-4613
Author(s):  
Sohaib Ahmad ◽  
◽  
Sardar Hussain ◽  
Muhammad Aamir ◽  
Faridoon Khan ◽  
...  
Keyword(s):  
Random Sampling ◽  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Sample Mean ◽  
Population Mean ◽  
New Family ◽  
Variable Bias ◽  
Mean Square Errors ◽  
The Given

<abstract><p>This paper addresses the issue of estimating the population mean for non-response using simple random sampling. A new family of estimators is proposed for estimating the population mean with auxiliary information on the sample mean and the rank of the auxiliary variable. Bias and mean square errors of existing and proposed estimators are obtained using the first order of measurement. Theoretical comparisons are made of the performance of the proposed and existing estimators. We show that the proposed family of estimators is more efficient than existing estimators in the literature under the given constraints using these theoretical comparisons.</p></abstract>

scholarly journals Use of Nonconventional Dispersion Measures to Improve the Efficiency of Ratio-Type Estimators of Variance in the Presence of Outliers

Symmetry ◽  
2019 ◽  
Vol 12 (1) ◽  
pp. 16 ◽  
Author(s):  
Farah Naz ◽  
Tahir Nawaz ◽  
Tianxiao Pang ◽  
Muhammad Abid
Keyword(s):  
Auxiliary Information ◽  
Simple Random Sampling ◽  
Auxiliary Variable ◽  
Auxiliary Variables ◽  
Absolute Deviation ◽  
Gini Mean Difference ◽  
Skewness Coefficient ◽  
Probability Weighted Moment ◽  
Dispersion Measures ◽  
Coefficient Of Skewness

The use of auxiliary information in survey sampling to enhance the efficiency of the estimators of population parameters is a common phenomenon. Generally, the ratio and regression estimators are developed by using the known information on conventional parameters of the auxiliary variables, such as variance, coefficient of variation, coefficient of skewness, coefficient of kurtosis, or correlation between the study and auxiliary variable. The efficiency of these estimators is dubious in the presence of outliers in the data and a nonsymmetrical population. This study presents improved variance estimators under simple random sampling without replacement with the assumption that the information on some nonconventional dispersion measures of the auxiliary variable is readily available. These auxiliary variables can be the inter-decile range, sample inter-quartile range, probability-weighted moment estimator, Gini mean difference estimator, Downton’s estimator, median absolute deviation from the median, and so forth. The algebraic expressions for the bias and mean square error of the proposed estimators are obtained and the efficiency conditions are derived to compare with the existing estimators. The percentage relative efficiencies are used to numerically compare the results of the proposed estimators with the existing estimators by using real datasets, indicating the supremacy of the suggested estimators.

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 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

Sign in / Sign up

Export Citation Format

Share Document