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

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), 2022. Published by Science Publishing Group

Keywords

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

References
[1] Bahl, S. and Tuteja, R. K. (1991). Ratio and product type exponential estimator. Journal of Information and Optimization Sciences, 12 (1), 159-163.
[2] Bhushan, S., Misra, P. K., and Yadav, S. K. (2017). On the class of double sampling exponential ratio type estimator using auxiliary information on an attribute and an auxiliary variable. International Journal of Computational and Applied Mathematics, 12 (1), 1-10.
[3] Clement, E. P., and Enang, E. I. (2017). On the efficiency of ratio estimator over the regression estimator. Communications in Statistics-Theory and Methods, 46 (11), 5357-5367.
[4] Cochran, W. G. (1977). Sampling techniques. John Wiley & Sons, New York.
[5] Deville, J. C., and Sarndal, C. E. (1992). Calibration estimators in survey sampling. Journal of the American Statistical Association, 87 (418), 376-382.
[6] Garg, N., and M. Pachori (2019). Calibration estimation of population mean in stratified sampling using coefficient of skewness. International Journal of Agricultural and Statistical Sciences, 15 (1), 211-219.
[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.
[9] Garg, N. and Pachori, M. (2022). Log type calibration estimator of population mean in stratified sampling. Journal of Indian Society of Probability and Statistics, 23, 19-45.
[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.
[11] Kim, J-M, Sungur, E. A., and Heo T-Y. (2007). Calibration approach estimators in stratified sampling. Statistics and Probability Letter, 77, 99-103.
[12] Koyuncu, N., and Kadilar, C. (2013). Calibration estimator using different distance measures in stratified random sampling. International Journal of Modern Engineering Research, 3 (1), 415-419.
[13] Koyuncu, N., and Kadilar, C. (2016). Calibration weighting in stratified random sampling. Communications in Statistics-Simulation and Computation, 45 (7), 2267-2275.
[14] Malik S., Singh, V. K., and Singh, R. (2014). An Improved Estimator for Population Mean using Auxiliary Information in Stratified Random Sampling. Statistics in Transition-New Series, 15 (1), 59–66.
[15] Mouhamed, A. M., EI-sheikh, A. A., and Mohamed, H. A. (2015). A new calibration estimator of Stratified random sampling. Applied Mathematical Sciences, 9 (35), 1735-1744.
[16] Onyeka, A. C. (2013). A class of product-type exponential estimators of the population mean in simple random sampling scheme. Statistics in Transitions, 14 (2), 189-200.
[17] Rashid, R., Amin, M. N., and Hanif, M. (2015). Exponential estimators for population mean using the transformed auxiliary variables. Applied Mathematics & Information Sciences, 9 (4), 2107-2112.
[18] Sarndal, C. E., Swensson, B., and Wretman, J. (2003). Model assisted survey sampling. Springer Verlag, New York.
[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.
[20] Singh, H. P., and Vishwakarma, G. K. (2007). Modified exponential ratio and product estimators for finite population mean in double sampling. Austrian Journal of Statistics, 36 (3), 217-225.
[21] Singh, S., and Arnab, R. (2011). On Calibration of design weights. METRON - International Journal of Statistics, LXIX (2), 185-205.
[22] Singh, S. (2003). Golden jubilee year 2003 of the linear regression estimator. Working paper at St. Cloud State University, St. Cloud, MN, USA.
[23] Tailor, R., Tailor, R., and Chouhan, S. (2017). Improved ratio and product-type exponential estimators for population mean in case of post-stratification. Communications in Statistics-Theory and Methods, 46 (21), 10387-10393.
[24] Tracy, D. S., Singh, S., and Arnab, R. (2003). Note on Calibration in Stratified and Double Sampling. Survey Methodology, 29 (1), 99-104.
Cite This Article
  • 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
  • School of Sciences, Indira Gandhi National Open University, New Delhi, India

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

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