Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach

Menakshi Pachori; Neha Garg

doi:doi:10.11648/j.ajtas.20221106.16

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Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach

Menakshi Pachori, Neha Garg

Published in American Journal of Theoretical and Applied Statistics (Volume 11, Issue 6)

Received: 21 November 2022 Accepted: 13 December 2022 Published: 23 December 2022

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Abstract

Calibration is a well-known technique for weight adjustment using various sets of constraints. This paper considers exponential ratio-type calibrated estimators for finite population mean using first three moments about the origin of the auxiliary variable in the calibration constraint under stratified random sampling. The exponential mean-type estimators for the second and third order moments are also suggested for the mentioned sampling scheme. When first three moments of the auxiliary variable are not known, then we use stratified double sampling scheme to estimate these moments. Thus, the result has been extended in the case of stratified double sampling and exponential mean-type and exponential ratio-type estimators have been developed using first three moments about the origin in the calibration constraints. The expression for mean squared error for the suggested estimators have been derived using the Taylor linearization method. For judging the performance of the proposed estimators, a simulation study has been carried out on two real datasets of MU284 population using R-software and their percentage root mean squared error (%RRMSE) and relative efficiency have been computed. The suggested estimators have been compared with the existing estimators given in the same setup and the new developed estimators are found to be more efficient than these estimators for the considered datasets.

Published in	American Journal of Theoretical and Applied Statistics (Volume 11, Issue 6)
DOI	10.11648/j.ajtas.20221106.16
Page(s)	225-237
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Auxiliary Information, Calibration Estimation, Stratified Random Sampling, Mean, Moments, Exponential Type Estimator

References

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[7]	Garg, N., and Pachori, M. (2020). Use of coefficient of variation in calibration estimation of population mean in stratified sampling. Communication in Statistics-Theory Methods, 49 (23), 5842−5852.
[8]	Garg, N., and Pachori, M. (2021). A Logarithmic calibration estimator of population mean in stratified double sampling. International Journal of Agricultural and Statistical Sciences, 17 (1), 2019-2025.
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[10]	Kadilar, G. O. (2016). A new exponential type estimator for the population mean in simple random sampling. Journal of Modern Applied Statistical Methods, 15 (2), 207-214.
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[19]	Singh, D., Sisodia, B. V. S., Rai, V. N., and Kumar, S. (2017). A calibration approach-based regression and ratio type estimators of finite population mean in two-stage stratified random sampling. Journal of the Indian Society of Agricultural Statistics, 71 (3), 217-224.
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APA Style

Menakshi Pachori, Neha Garg. (2022). Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach. American Journal of Theoretical and Applied Statistics, 11(6), 225-237. https://doi.org/10.11648/j.ajtas.20221106.16

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ACS Style

Menakshi Pachori; Neha Garg. Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach. Am. J. Theor. Appl. Stat. 2022, 11(6), 225-237. doi: 10.11648/j.ajtas.20221106.16

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AMA Style

Menakshi Pachori, Neha Garg. Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach. Am J Theor Appl Stat. 2022;11(6):225-237. doi: 10.11648/j.ajtas.20221106.16

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@article{10.11648/j.ajtas.20221106.16,
  author = {Menakshi Pachori and Neha Garg},
  title = {Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {6},
  pages = {225-237},
  doi = {10.11648/j.ajtas.20221106.16},
  url = {https://doi.org/10.11648/j.ajtas.20221106.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221106.16},
  abstract = {Calibration is a well-known technique for weight adjustment using various sets of constraints. This paper considers exponential ratio-type calibrated estimators for finite population mean using first three moments about the origin of the auxiliary variable in the calibration constraint under stratified random sampling. The exponential mean-type estimators for the second and third order moments are also suggested for the mentioned sampling scheme. When first three moments of the auxiliary variable are not known, then we use stratified double sampling scheme to estimate these moments. Thus, the result has been extended in the case of stratified double sampling and exponential mean-type and exponential ratio-type estimators have been developed using first three moments about the origin in the calibration constraints. The expression for mean squared error for the suggested estimators have been derived using the Taylor linearization method. For judging the performance of the proposed estimators, a simulation study has been carried out on two real datasets of MU284 population using R-software and their percentage root mean squared error (%RRMSE) and relative efficiency have been computed. The suggested estimators have been compared with the existing estimators given in the same setup and the new developed estimators are found to be more efficient than these estimators for the considered datasets.},
 year = {2022}
}

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TY  - JOUR
T1  - Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach
AU  - Menakshi Pachori
AU  - Neha Garg
Y1  - 2022/12/23
PY  - 2022
N1  - https://doi.org/10.11648/j.ajtas.20221106.16
DO  - 10.11648/j.ajtas.20221106.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 225
EP  - 237
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20221106.16
AB  - Calibration is a well-known technique for weight adjustment using various sets of constraints. This paper considers exponential ratio-type calibrated estimators for finite population mean using first three moments about the origin of the auxiliary variable in the calibration constraint under stratified random sampling. The exponential mean-type estimators for the second and third order moments are also suggested for the mentioned sampling scheme. When first three moments of the auxiliary variable are not known, then we use stratified double sampling scheme to estimate these moments. Thus, the result has been extended in the case of stratified double sampling and exponential mean-type and exponential ratio-type estimators have been developed using first three moments about the origin in the calibration constraints. The expression for mean squared error for the suggested estimators have been derived using the Taylor linearization method. For judging the performance of the proposed estimators, a simulation study has been carried out on two real datasets of MU284 population using R-software and their percentage root mean squared error (%RRMSE) and relative efficiency have been computed. The suggested estimators have been compared with the existing estimators given in the same setup and the new developed estimators are found to be more efficient than these estimators for the considered datasets.
VL  - 11
IS  - 6
ER  -

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Author Information

Menakshi Pachori

School of Sciences, Indira Gandhi National Open University, New Delhi, India
Neha Garg

School of Sciences, Indira Gandhi National Open University, New Delhi, India

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APA Style

Menakshi Pachori, Neha Garg. (2022). Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach. American Journal of Theoretical and Applied Statistics, 11(6), 225-237. https://doi.org/10.11648/j.ajtas.20221106.16

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ACS Style

Menakshi Pachori; Neha Garg. Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach. Am. J. Theor. Appl. Stat. 2022, 11(6), 225-237. doi: 10.11648/j.ajtas.20221106.16

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AMA Style

Menakshi Pachori, Neha Garg. Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach. Am J Theor Appl Stat. 2022;11(6):225-237. doi: 10.11648/j.ajtas.20221106.16

Copy | Download

@article{10.11648/j.ajtas.20221106.16,
  author = {Menakshi Pachori and Neha Garg},
  title = {Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach},
  journal = {American Journal of Theoretical and Applied Statistics},
  volume = {11},
  number = {6},
  pages = {225-237},
  doi = {10.11648/j.ajtas.20221106.16},
  url = {https://doi.org/10.11648/j.ajtas.20221106.16},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ajtas.20221106.16},
  abstract = {Calibration is a well-known technique for weight adjustment using various sets of constraints. This paper considers exponential ratio-type calibrated estimators for finite population mean using first three moments about the origin of the auxiliary variable in the calibration constraint under stratified random sampling. The exponential mean-type estimators for the second and third order moments are also suggested for the mentioned sampling scheme. When first three moments of the auxiliary variable are not known, then we use stratified double sampling scheme to estimate these moments. Thus, the result has been extended in the case of stratified double sampling and exponential mean-type and exponential ratio-type estimators have been developed using first three moments about the origin in the calibration constraints. The expression for mean squared error for the suggested estimators have been derived using the Taylor linearization method. For judging the performance of the proposed estimators, a simulation study has been carried out on two real datasets of MU284 population using R-software and their percentage root mean squared error (%RRMSE) and relative efficiency have been computed. The suggested estimators have been compared with the existing estimators given in the same setup and the new developed estimators are found to be more efficient than these estimators for the considered datasets.},
 year = {2022}
}

Copy | Download

TY  - JOUR
T1  - Exponential Mean and Ratio-Types Estimators of Population Mean Using Moments Under Calibration Approach
AU  - Menakshi Pachori
AU  - Neha Garg
Y1  - 2022/12/23
PY  - 2022
N1  - https://doi.org/10.11648/j.ajtas.20221106.16
DO  - 10.11648/j.ajtas.20221106.16
T2  - American Journal of Theoretical and Applied Statistics
JF  - American Journal of Theoretical and Applied Statistics
JO  - American Journal of Theoretical and Applied Statistics
SP  - 225
EP  - 237
PB  - Science Publishing Group
SN  - 2326-9006
UR  - https://doi.org/10.11648/j.ajtas.20221106.16
AB  - Calibration is a well-known technique for weight adjustment using various sets of constraints. This paper considers exponential ratio-type calibrated estimators for finite population mean using first three moments about the origin of the auxiliary variable in the calibration constraint under stratified random sampling. The exponential mean-type estimators for the second and third order moments are also suggested for the mentioned sampling scheme. When first three moments of the auxiliary variable are not known, then we use stratified double sampling scheme to estimate these moments. Thus, the result has been extended in the case of stratified double sampling and exponential mean-type and exponential ratio-type estimators have been developed using first three moments about the origin in the calibration constraints. The expression for mean squared error for the suggested estimators have been derived using the Taylor linearization method. For judging the performance of the proposed estimators, a simulation study has been carried out on two real datasets of MU284 population using R-software and their percentage root mean squared error (%RRMSE) and relative efficiency have been computed. The suggested estimators have been compared with the existing estimators given in the same setup and the new developed estimators are found to be more efficient than these estimators for the considered datasets.
VL  - 11
IS  - 6
ER  -

Copy | Download