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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Main Authors: Saddam Hussain, Mi Zichuan, Sardar Hussain, Anum Iftikhar, Muhammad Asif, Sohail Akhtar, Sohaib Ahmad
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Probability and Statistics
Online Access:http://dx.doi.org/10.1155/2020/1693612
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spelling 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
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