On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling
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...
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doaj-13e67414e9e342dda7866e21b904e3f62020-11-25T02:46:39ZengHindawi LimitedJournal of Probability and Statistics1687-952X1687-95382020-01-01202010.1155/2020/16936121693612On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random SamplingSaddam Hussain0Mi Zichuan1Sardar Hussain2Anum Iftikhar3Muhammad Asif4Sohail Akhtar5Sohaib Ahmad6Department of Statistics, Shanxi University of Finance and Economics, Taiyuan, ChinaDepartment of Statistics, Shanxi University of Finance and Economics, Taiyuan, ChinaDepartment of Statistics, Quaid-i-Azam University, Islamabad, PakistanDepartment of Statistics, Shanxi University of Finance and Economics, Taiyuan, ChinaDepartment of Statistics University of Malakand, Chakdara, PakistanDepartment of Statistics Government College University Lahore, Lahore, PakistanDepartment of Statistics, Quaid-i-Azam University, Islamabad, PakistanIn 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.http://dx.doi.org/10.1155/2020/1693612 |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Saddam Hussain Mi Zichuan Sardar Hussain Anum Iftikhar Muhammad Asif Sohail Akhtar Sohaib Ahmad |
spellingShingle |
Saddam Hussain Mi Zichuan Sardar Hussain Anum Iftikhar Muhammad Asif Sohail Akhtar Sohaib Ahmad On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling Journal of Probability and Statistics |
author_facet |
Saddam Hussain Mi Zichuan Sardar Hussain Anum Iftikhar Muhammad Asif Sohail Akhtar Sohaib Ahmad |
author_sort |
Saddam Hussain |
title |
On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling |
title_short |
On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling |
title_full |
On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling |
title_fullStr |
On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling |
title_full_unstemmed |
On Estimation of Distribution Function Using Dual Auxiliary Information under Nonresponse Using Simple Random Sampling |
title_sort |
on estimation of distribution function using dual auxiliary information under nonresponse using simple random sampling |
publisher |
Hindawi Limited |
series |
Journal of Probability and Statistics |
issn |
1687-952X 1687-9538 |
publishDate |
2020-01-01 |
description |
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. |
url |
http://dx.doi.org/10.1155/2020/1693612 |
work_keys_str_mv |
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