• P-ISSN 0974-6846 E-ISSN 0974-5645

Indian Journal of Science and Technology

Article

Indian Journal of Science and Technology

Year: -0001, Volume: 15, Issue: 7, Pages: 276-291

Original Article

An Improved Class of Mixed Estimators of Population Mean under Double Sampling

Received Date:29 July 2021, Accepted Date:05 January 2022, Published Date:30 November -0001

Abstract

Objectives: To estimate the finite populations mean using two auxiliary variables in double sampling as well as the efficiency of the proposed class of estimators. Methods: The mixing of estimators became more popular in developing more efficient estimators for estimating finite population parameters but while mixing two or more estimators, we should consider the basic purpose and the conditions under which the individual estimators are developed and are efficient. This paper deals with a class of mixed estimators of population mean by mixing ratio estimator and dual to product estimator in two phase sampling scheme using SRSWOR scheme to select the sample units at both the cases, i.e. Case-I: When 􀀀 X is unknown but 􀀀 Z is known and Case-II: When both 􀀀 X and 􀀀 Z are unknown. The purpose of mixing these two estimators is that both these estimators are designed to be used effectively for population mean when the population correlation coefficient between the study variable and the auxiliary variable is highly positive. Results: We observe that the proposed class of estimators is more efficient than the existing estimators which are available in literature and the empirical study indicates that the proposed class of estimators t01 and t02 performs better than the other existing estimators of t ′ 1; t ′ 2; t ′ 3; t ′ 4; t ′ 5; t ′ 6; t ′ 7; t ′ 8 and t ′ 9. Novelty: The percent relative efficiency (PRE) of the proposed class of estimators in Case-II i.e., t02 is superior than the estimator proposed in Case-I t01 for all the populations except Population 1 and 10, which needs further rigorous attention to compare the performances of t01 and t02:

Keywords: Double sampling; Class of estimators; Bias; Mean square error (MSE); Percent relative efficiency (PRE)

References

  1. Zaman T, Kadilar C. New class of exponential estimators for finite population mean in two-phase samplingCommunications in Statistics - Theory and Methods2021;50(4):874889. doi: 10.1080/03610926.2019.1643480
  2. Kumar M, Bahl S. Class of dual to ratio estimators for double samplingStatistical Papers2006;47(2):319326. doi: 10.1007/s00362-005-0291-6
  3. Singh B, Kumar C, Sanjib. Dual to Product Estimator for Estimating Population Mean in Double SamplingInternational Journal of Statistics and Systems2012;7(1):3139.
  4. Chanu Waikhom WarseenSingh BhupendraKumar. Improved Class of Ratio-cum-Product Estimators of Finite Population Mean in Two-Phase SamplingGlobal Journal of Science Frontier Research2014;p. 6981.
  5. Choudhury S, Singh BK. Study of Dual to Ratio-Cum-Product Estimator of Finite Population Mean under Double Sampling in Sample SurveysJournal of Statistical Theory and Applications2015;14(2):214. doi: 10.2991/jsta.2015.14.2.9
  6. Bandyopadhyay A, Singh GN. Predictive estimation of population mean in two-phase samplingCommunications in Statistics - Theory and Methods2016;45(14):42494267. doi: 10.1080/03610926.2014.919396
  7. Guha S, Chandra H. Improved chain-ratio type estimator for population total in double samplingMathematical Population Studies2020;27(4):216231. doi: 10.1080/08898480.2019.1626635
  8. Sunil K, Vishwantra S. Improved Chain Ratio-Product Type Estimators Under Double Sampling SchemeJournal of Statistics Applications & Probability Letters2020;7(2):8796.
  9. Kamal A, Amir N, Dastagir H. Some Exponential Type Predictive Estimators of Finite Population Mean in Two-Phase SamplingSTATISTICS, COMPUTING AND INTERDISCIPLINARY RESEARCH2020;2(1):5157. doi: 10.52700/scir.v2i1.10
  10. Zaman T. An efficient exponential estimator of the mean under stratified random samplingMathematical Population Studies2021;28(2):104121. doi: 10.1080/08898480.2020.1767420
  11. Sanjib C, Singh BhupendraKumar. 2012. Available from: https://www.researchgate.net/publication/235939061
  12. Misra P, Tiwari N, Ahuja TK. An Enhanced Two Phase Sampling Ratio Estimator for Estimating Population MeanJournal of Scientific Research2021;65(03):177183. doi: 10.37398/jsr.2021.650321
  13. Lynch TB, Gove JH, Gregoire TG, Ducey MJ. An approximate point-based alternative for the estimation of variance under big BAF samplingForest Ecosystems2021;8(1). doi: 10.1186/s40663-021-00304-0
  14. Balamurali S, Aslam M, Ahmad L, Jun CH. A mixed double sampling plan based on CpkCommunications in Statistics - Theory and Methods2020;49(8):18401857. doi: 10.1080/03610926.2019.1565836
  15. Hassan Y, Ismail M, Murray W, Qaiser Shahbaz M. Efficient estimation combining exponential and ln functions under two phase samplingAIMS Mathematics2020;5(6):76047622.
  16. Jabeen R Sanaullah A, Hanif M, Zaka A et al. Two-exponential estimators for estimating population meanAIMS Mathematics2021;6(1):737753. doi: 10.3934/math.2021045
  17. Ahmad S, Arslan M, Khan A, Shabbir J. A generalized exponential-type estimator for population mean using auxiliary attributesPLOS ONE2021;16(5):e0246947. doi: 10.1371/journal.pone.0246947
  18. Singh B, Kumar K, Nath. Some Imputation Methods in Two-Phase Sampling Scheme for Estimation of Population MeanResearch & Reviews: Journal of Statistics2018;7(1):116.
  19. Yadav SK, Zaman T. Use of some conventional and non-conventional parameters for improving the efficiency of ratio-type estimatorsJournal of Statistics and Management Systems2021;24(5):10771100. doi: 10.1080/09720510.2020.1864939
  20. Zaman T Kadilar C, . Exponential ratio and product type estimators of the mean in stratified two-phase samplingAIMS Mathematics2021;6(5):42654279. doi: 10.3934/math.2021252
  21. Zaman T, Dünder E. Proposing Novel Modified Ratio Estimators by Adding an Exponential ParameterLobachevskii Journal of Mathematics2020;41(3):451458. doi: 10.1134/s1995080220030208
  22. Zaman T. Generalized exponential estimators for the finite population meanStatistics in Transition New Series2020;21(1):159168. doi: 10.21307/stattrans-2020-009

Copyright

© 2022 Dash & Sunani. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Published By Indian Society for Education and Environment (iSee)

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