Two Phase Adaptive Cluster Sampling Under Transformed Population Approach

Raghav, Yashpal Singh; Singh, Rajesh; Mishra, Rohan; Ahmadini, Abdullah Ali H.; Adichwal, Nitesh Kumar; Ali, Irfan

doi:10.1134/S1995080224600237

Two Phase Adaptive Cluster Sampling Under Transformed Population Approach

Published: 14 May 2024

Volume 45, pages 770–793, (2024)
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Lobachevskii Journal of Mathematics Aims and scope Submit manuscript

Yashpal Singh Raghav¹,
Rajesh Singh²,
Rohan Mishra²,
Abdullah Ali H. Ahmadini¹,
Nitesh Kumar Adichwal³ &
…
Irfan Ali⁴

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Abstract

In survey sampling, it might happen that information on the population mean of the auxiliary variable is not available, but it can be obtained if the researcher opts for it. The sampling design to be used in such a case is the Two-Phase sampling design. This design has been studied extensively in SRSWOR, but it has not been studied when the population under study is rare or clumped. It is known that when the population under study is rare or clumped, adaptive cluster sampling (ACS) design is more efficient, and therefore in this paper we have proposed the Two-Phase Adaptive Cluster Sampling Under Transformed Population Approach and further proposed ratio and product estimator and a generalized robust ratio type estimator in this design. The bias and MSE of the proposed estimators have been derived and presented up to the first order of approximation. Further, the performance of the proposed estimators has been analyzed using simulation studies.

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Funding

This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.

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Authors and Affiliations

Department of Mathematics, Faculty of Science, Jazan University, Jazan, Saudi Arabia
Yashpal Singh Raghav & Abdullah Ali H. Ahmadini
Department of Statistics, Institute of Science, Banaras Hindu University, Varanas, Uttar Pradesh, India
Rajesh Singh & Rohan Mishra
Department of General Management, University of Petroleum and Energy Studies, 248007, Bidholi, Uttarakhand, India
Nitesh Kumar Adichwal
Department of Statistics and Operations Research, Aligarh Muslim University, 202001, Aligarh, Uttar Pradesh, India
Irfan Ali

Authors

Yashpal Singh Raghav
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Rajesh Singh
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Rohan Mishra
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Abdullah Ali H. Ahmadini
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Nitesh Kumar Adichwal
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Irfan Ali
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Correspondence to Irfan Ali.

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APPENDIX

Population of auxiliary variable \(X\) taken from [23]

0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	14	25	2
0	0	0	0	0	0	0	22	38	3
0	0	0	0	0	0	2	2	6	1
0	0	0	0	0	0	0	0	0	0
0	1	1	1	0	0	0	0	0	0
2	11	26	5	0	0	0	0	0	0
2	22	19	8	0	0	0	0	0	0
0	3	5	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	1	1	0	0	0	0
0	0	0	17	26	9	0	0	0	0
0	0	1	10	26	6	0	0	0	0
0	0	0	5	2	1	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0

Population of survey variable Y of population 1

0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	25	25	5
0	0	0	0	0	0	0	27	34	1
0	0	0	0	0	0	4	4	6	1
0	0	0	0	0	0	0	0	0	0
0	0	3	2	0	0	0	0	0	0
3	7	68	2	0	0	0	0	0	0
4	70	37	14	0	0	0	0	0	0
0	3	5	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	3	2	0	0	0	0
0	0	0	14	37	14	0	0	0	0
0	0	1	20	35	14	0	0	0	0
0	0	0	9	3	2	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0

Population of survey variable Y of population 2

0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	53	75	9
0	0	0	0	0	0	0	71	110	7
0	0	0	0	0	0	8	8	18	3
0	0	0	0	0	0	0	0	0	0
0	2	5	4	0	0	0	0	0	0
7	29	120	12	0	0	0	0	0	0
8	114	75	30	0	0	0	0	0	0
0	9	15	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	5	4	0	0	0	0
0	0	0	48	89	32	0	0	0	0
0	0	3	40	87	26	0	0	0	0
0	0	0	19	7	4	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0

Population of survey variable Y of population 3

0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	81	125	13
0	0	0	0	0	0	0	115	186	13
0	0	0	0	0	0	12	12	30	5
0	0	0	0	0	0	0	0	0	0
0	4	7	6	0	0	0	0	0	0
11	51	172	22	0	0	0	0	0	0
12	158	113	46	0	0	0	0	0	0
0	15	25	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	7	6	0	0	0	0
0	0	0	82	141	50	0	0	0	0
0	0	5	60	139	38	0	0	0	0
0	0	0	29	11	6	0	0	0	0
0	0	0	0	0	0	0	0	0	0
0	0	0	0	0	0	0	0	0	0

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Raghav, Y.S., Singh, R., Mishra, R. et al. Two Phase Adaptive Cluster Sampling Under Transformed Population Approach. Lobachevskii J Math 45, 770–793 (2024). https://doi.org/10.1134/S1995080224600237

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Received: 06 March 2023
Revised: 19 March 2023
Accepted: 30 March 2023
Published: 14 May 2024
Issue Date: February 2024
DOI: https://doi.org/10.1134/S1995080224600237

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Two Phase Adaptive Cluster Sampling Under Transformed Population Approach

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Publisher’s Note.

APPENDIX

APPENDIX

Population of auxiliary variable \(X\) taken from [23]

Population of survey variable Y of population 1

Population of survey variable Y of population 2

Population of survey variable Y of population 3

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