International Research Journal of Innovations in Engineering and Technology - IRJIET International Open Access, Monthly, Peer Reviewed, Reputed Journal ISSN (online): 2581-3048

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DOI Prefix: 10.47001/IRJIET

Efficient Class of Ratio–Cum–Product Estimator of Population Mean in Two Phase Sampling in Presence of Two Auxiliary Variables with Application to Agricultural Data Sets

Etorti Imoke JohnDepartment of Mathematics, School of Secondary Education Science programmes, Cross River State College of Education, Akamkpa-NigeriaAgada Anthony NwachuyaDepartment of Mathematics, School of Secondary Education Science programmes, Cross River State College of Education, Akamkpa-Nigeria

Vol 8 No 1 (2024): Volume 8, Issue 1, January 2024 | Pages: 128-150

International Research Journal of Innovations in Engineering and Technology

OPEN ACCESS | Research Article | Published Date: 31-01-2024

doi Logo doi.org/10.47001/IRJIET/2024.801017

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Abstract

In order to minimize errors in survey estimation situation, it is imperative that we adopt a sampling method that is capable of giving an improved results and which will be adjudged to be a better representation of the population. In this study, efficient class of ratio–cum-product estimators of population mean Y-  in Two Phase Sampling in presence of two auxiliary variables x and z was proposed. Members of the proposed class of estimator were obtained by varying the scalars associated with the proposed estimator, from where it was observed that the estimator produces the traditional sample mean ratio estimator Y- , the dual to Singh and Tailor (2005) estimator due to Tailor et al (2012), Singh and Tailor (2011) generalized version of the dual to ratio-cum-product estimator of the population mean Y-. Various attribute of the proposed estimator such as biases, relative biases, Mean Square Errors (MSEs), and optimal MSEs were derived for cases I and II to the quadratic form of Tailor’s series approximation. Theoretical proposition for evaluating efficiency was established and empirical study was conducted using Four (4) Agricultural data sets to ascertain the veracity of the theoretical proposition, from where it was found out from the results that the estimators TDS1TDS3, TDS4, TDS5 and TDS12, were more efficient in case I and estimators’ T*DS1T*DS3, T*DS4, T*DS4T*DS9, T*DS12 and T*DS13 were more efficient in case II, having been ascertained to have produced smaller MSEs. The gain in efficiency increases as the sample size decreases and was more significant in case II. Therefore, sub-sampling the second sample independent of the first sample is advantageous and recommended for appreciable gain in efficiency and superiority over the first phase in double sampling scheme.

Keywords

Efficiency, Estimator, Double Sampling and Population Mean


Citation of this Article

Etorti Imoke John, Agada Anthony Nwachuya, “Efficient Class of Ratio–Cum–Product Estimator of Population Mean in Two Phase Sampling in Presence of Two Auxiliary Variables with Application to Agricultural Data Sets” Published in International Research Journal of Innovations in Engineering and Technology - IRJIET, Volume 8, Issue 1, pp 128-150, January 2024. Article DOI https://doi.org/10.47001/IRJIET/2024.801017

Licence Copyright (c) 2026 International Research Journal of Innovations in Engineering and Technology creative common licence This work is licensed under Creative common Attribution Non Commercial 4.0 Internation Licence
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