Use of Known Parameters of Auxiliary Variable for Mean Estimation in Successive Sampling Over Two Occasions

Deepak Majhi; Uttam Kumar Prasad

doi:https://doi.org/10.14445/22315373/IJMTT-V72I4P112

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 72 | Issue 4 | Year 2026 | Article Id. IJMTT-V72I4P112 | DOI : https://doi.org/10.14445/22315373/IJMTT-V72I4P112

Use of Known Parameters of Auxiliary Variable for Mean Estimation in Successive Sampling Over Two Occasions

Deepak Majhi, Uttam Kumar Prasad

Received	Revised	Accepted	Published
28 Feb 2026	31 Mar 2026	22 Apr 2026	30 Apr 2026

Citation :

Deepak Majhi, Uttam Kumar Prasad, "Use of Known Parameters of Auxiliary Variable for Mean Estimation in Successive Sampling Over Two Occasions," International Journal of Mathematics Trends and Technology (IJMTT), vol. 72, no. 4, pp. 83-92, 2026. Crossref, https://doi.org/10.14445/22315373/IJMTT-V72I4P112

Abstract

This study takes a look at the issue of estimating the population means on this particular occasion using samples taken on two separate dates. The characteristics of three possible estimators are presented and examined, all of which rely on the known coefficients of variation, skewness, and kurtosis. We have spoken about the best practices for replacing the estimators. We have compared the suggested estimators to the optimal estimator, which is a linear combination of the means of the matched and unmatched sections of the sample on this occasion, and to the sample mean estimate when no matching is present.

Keywords

Auxiliary information, Bias, Mean Square Error, Optimum replacement strategy, Mathematics subject classification – 62D05.

References

[1] Raymond James Jessen, “Statistical Investigation of a Sample Survey for Obtaining Farm Facts,” Iowa Agricultural Experiment Station Research Bulletin No. 304, Ames, Iowa, 1943.
[Google Scholar] [Publisher Link]

[2] H.D. Patterson, “Sampling on Successive Occasions with Partial Replacement of Units,” Journal of the Royal Statistical Society, vol. 12, no. 2, pp. 241-255, 1950.
[Google Scholar] [Publisher Link]

[3] J.N.K. Rao, and Jack E. Graham, “Rotation Design for Sampling on Repeated Occasions,” Journal of the American Statistical Association, vol. 59, no. 306, pp. 492-509, 1964.
[Google Scholar] [Publisher Link]

[4] P.C. Gupta, “Sampling on Two Successive Occasions,” Journal of Statistical Research, vol. 13, pp. 7-16, 1979.
[Google Scholar]

[5] A.K. Das, “Estimation of Population Ratio on Two Occasions,” Journal of Indian Society of Agricultural Statistics, vol. 34, pp. 1-9, 1982.
[Google Scholar]

[6] D.K. Chaturvedi, and T.P. Tripathi, “Estimation of Population Ratio on Two Occasions using Multivariate Auxiliary Information,” Journal of Indian Statistical Association, vol. 21, pp. 113-120, 1983.
[Google Scholar]

[7] A.R. Sen, “Successive Sampling with Two Auxiliary Variables,” Sankhya: The Indian Journal of Statistics, Series B, vol. 33, no. 3/4, pp. 371-378, 1971.
[Google Scholar] [Publisher Link]

[8] A.R. Sen, “Successive Sampling with p Auxiliary Variables,” The Annals of Mathematical Statistics, vol. 43, no. 6, pp. 2031-2034, 1972.
[Google Scholar] [Publisher Link]

[9] A.R. Sen, “Theory and Application of Sampling on Repeated Occasions with Several Auxiliary Variables,” Biometrics, vol. 29, no. 2, pp. 381-385, 1973.
[CrossRef] [Google Scholar] [Publisher Link]

[10] V.K. Singh, G.N. Singh, and D. Shukla, “An Efficient Family of Ratio-Cum-Difference Type Estimators in Successive Sampling Over Two Occasions,” Journal of Science Research, vol. 41, pp. 149-159, 1991.
[Google Scholar]

[11] Garib Nath Singh, and Vijay Kumar Singh, “On the use of Auxiliary Information in Successive Sampling,” Journal Indian Society Agricultural Statistics, vol. 54, no. 1, pp. 1-12, 2001.
[Google Scholar]

[12] G.N. Singh, “Estimation of Population Mean using Auxiliary Information on Recent Occasion in H-occasion Successive Sampling,” Statistics in Transition, vol. 6, no. 4, pp. 523-532, 2003.
[Google Scholar]

[13] Shiyong Feng, and Guohua Zou, “Sample Rotation Method with Auxiliary Variable,” Communications in Statistics-Theory and Methods, vol. 26, no. 6, pp. 1497-1509, 1997.
[CrossRef] [Google Scholar] [Publisher Link]

[14] R.S. Biradar, and H.P. Singh, “Successive Sampling using Auxiliary Information on Both Occasions,” Calcutta Statistical Association Bulletin, vol. 51, no. 3-4, pp. 243-252, 2001.
[CrossRef] [Google Scholar] [Publisher Link]

[15] G.N. Singh, “On the use of Chain-type Ratio Estimator in Successive Sampling,” Statistics in Transition,” vol. 7, no. 1, pp. 21-26, 2005.
[Google Scholar]

[16] G.N. Singh, and Kumari Priyanka, “On the use of Chain-type Ratio to Difference Estimator in Successive Sampling,” International Journal of Applied Mathematics and Statistics, vol. 5, no. S06, 2006.
[Google Scholar] [Publisher Link]

[17] G.N. Singh, and Kumari Priyanka, “On the use of Auxiliary Information in Search of Good Rotation Patterns on Successive Occasions,’ International Journal of Statistics & Economics (Bulletin of Statistics and Economics), vol. 1, no. A07, pp. 42-60, 2007.
[Google Scholar]

[18] G.N. Singh, and Kumari Priyanka, “Search of Good Rotation Patterns to Improve the Precision of Estimates at Current Occasion,” Communications in Statistics- Theory and Methods, vol. 37, no. 3, pp. 337-348, 2008.
[CrossRef] [Google Scholar] [Publisher Link]

[19] Garib Nath Singh, and Jaishree Prabha Karna, “Estimation of Population Mean on the Current in Two- Occasion Successive Sampling,” Metron-International Journal of Statistics, vol. 67, no. 1, pp. 87-103, 2009.
[Google Scholar]

[20] Deepak Majhi, “A New Rotation Patterns in Successive Sampling over Two Occasions,” International Journal of Mathematics and Computation, vol. 29, no. 3, 2018.
[Publisher Link]

[21] Pandurang V. Sukhatme et al., Sampling Theory of Surveys with Applications, Iowa State University Press, Ames, Iowa (USA) and Indian Society of Agricultural Statistics, New Delhi (India), 1970.
[Google Scholar] [Publisher Link]