# Calibration Estimation for Ratio Estimators in Stratified Sampling for Proportion Allocation

Keywords:
Auxiliary Information; Calibration Approach; Estimation of Variance; Proportion Allocation; Ratio Estimator; Stratified Sampling.

### Abstract

Calibration has established itself as an important methodological instrument in large scale production of statistics. In this paper, we propose calibration estimation for ratio estimator in stratified sampling and derive the estimator of the variance of the calibration estimation ratio estimator in stratified sampling in case proportion allocation.

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### References

1- Al-Omari, A. (2012). Ratio estimation of the population mean using auxiliary information in simple random sampling and median ranked set sampling, Statistics and Probability Letters, 82(11), 1883-1890.

2- Amelia, V. (2013). Improvement on the non-response in the population ratio of mean for current occasion in sampling on two occasions. Pakistan Journal of Statistics and Operation Research, 9(1), 25-51.

3- Bahl, S. and Tuteja, R.K. (1991). Ratio and product type exponential estimator. Journal of Information and Optimization Science, 12(1), 159-164.

4- Chao, C.T ., Dryver, A.L. and Chiang, T.C. (2010). Leveraging the Rao–Blackwell theorem to improve ratio estimators in adaptive cluster sampling, Environmental and ecological statistics,18, 543–568. 5-Deville, J.C., and Sarndal, C. E. (1992). Calibration Estimators in Survey Sampling. JASA, 87, 376-382.

6-El-Sheikh, A.A. and Mohamed, H.A. (2013). Calibration estimation in stratified Sampling. The 48th Annual Conference on Statistics, Computer Sciences and Operation Research, Institute of Statistical Studies and Research, Cairo University, Egypt.

7- Hansen, M.H. and Hurwitz, W.N. (1943). On the theory of sampling from finite populations, Annals of Mathmatical Statistic. 14,333-362.

8- Housila, P. S. and Gajendra, K. V. (2007). Modified exponential ratio and product estimators for finite population mean in double sampling, Austrian Journal of Statistics , 36(3), 217–225.

9- Housila, P. S. and Ramkrishna, S. S. (2011). Generalized ratio and product methods of estimation in survey sampling. Pakistan Journal of Statistics and Operation Research, 7(2), 245-264.

10-Jozani, M.J. and Johnson, B.C., (2011). Design based estimation for ranked set sampling in finite populations. Environmental and ecological statistics, 18, 663–685.

11- Kadilar, C. and Cingi, H. (2003). Ratio estimators in stratified random sampling. Biometrical Journal, 45(2), 218-225

12- Kadilar, C. Unyazici, Y. and • Cingi, H. (2009). Ratio estimator for the population mean using ranked set sampling. Statistical Papers, 50,301–309.

13-Kim, J.M. Sungur, E.A and Heo, T-Y. (2006). Calibration approach estimators in stratified sampling. Statistics and Probability Letters, 77, 99–103.

14- Koyuncu, N., and Kadilar. C.(2010). On the family of estimators of population mean in stratified random sampling. Pakistan Journal of Statistics, 26(2), 427-443.

15- Luengo, V.G. (2016). Ratio-cum-product estimation in presence of non-response in successive sampling. Journal of Applied Mathematics, Statistics and Informatics, 12(1), 55-83.

16-Okafor, F.C., and Lee, H., (2000). Double sampling for ratio and regression estimation with subsampling the nonrespondents. Survey Methodology, Statistics Canada, 26(2), 183-188.

17- Prasad, B. (1989). Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Communications in Statistics-Theory and Methods, 18(1), 379-392.

18- Rodriguez, A., Eva, M. , Luengo, G. and Amelia. V. (2001). Estimation of current population ratio in successive sampling. Jour. Ind. Soc. Ag. Statistics, 54(3), 342-354.

19-Samawi, H.M, and Muttlak, H.A. (1996). Estimation of ratio using rank set sampling, Biometrical Journal, 38(6), 753-764.

20- Shahzad, U., Hanif, M., Koyuncu, N. and Luengo,. A.V.G., (2019). A Family of ratio estimators in stratified random sampling utilizing auxiliary attribute alongside the nonresponse issue, Journal of Statistical Theory and Applications, 18(1), 12–25.

21-Singh, S., Horn, S., Yu, F., (1998). Estimation of variance of the general regression estimator: higher level calibration approach. Survey Methodology, 24(1), 41–50.

22-Singh, H.P. and Kakran, M.S. (1993). A modified ratio estimator using known coefficient of kurtosis of an auxiliary character. Revised Version submitted to Journal of Indian Society of Agricultural Statistics, New Delhi, Endia

23-Singh, R., Kumar, M., Singh, R.D., and Chaudhary, M.K. (2008). Exponential ratio type estimators in stratified random sampling, Presented in International Symposium on Optimisation and Statistics (I.S.O.S) at A.M.U., Aligarh, India.

24-Singh, H. P., and Solanki, R. S. (2011). Generalized ratio and product methods of estimation in survey sampling, Pakistan Journal of Statistics and Operation Research, 7(2), 305-314.

25-Sisodia, B.V.S. and Dwivedi, V.K., (1981). A modified ratio estimator using coefficient of variation of auxiliary variable. J. Indian Soc. Agricultural Statist. 33, 13–18.

26- Sriven, T. and Tracy, D.S. (1979). On ratio and product methods of estimation in sampling. Statistica Neerlandica, 33(1), 37-49.

27- Swain, A. K. P. C. (2013). On some modified ratio And product type estimators. Revisted Revista Investgation Operacional , 34(1), 35-57.

28-Upadhyaya, L.N., Singh, H.P., (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical journal. 41,627–636.

29-Wu,C.F.J (1985). Variance Estimation for the combined ratio and combined regression estimators. Royal Statistical Society. 47(1), 147-154.

30-Zaizai,Y. (2006), Ratio method of estimation of population proportion using randomized response technique , Model Assisted Statistics and Applications, 1(2), 125-130.

2- Amelia, V. (2013). Improvement on the non-response in the population ratio of mean for current occasion in sampling on two occasions. Pakistan Journal of Statistics and Operation Research, 9(1), 25-51.

3- Bahl, S. and Tuteja, R.K. (1991). Ratio and product type exponential estimator. Journal of Information and Optimization Science, 12(1), 159-164.

4- Chao, C.T ., Dryver, A.L. and Chiang, T.C. (2010). Leveraging the Rao–Blackwell theorem to improve ratio estimators in adaptive cluster sampling, Environmental and ecological statistics,18, 543–568. 5-Deville, J.C., and Sarndal, C. E. (1992). Calibration Estimators in Survey Sampling. JASA, 87, 376-382.

6-El-Sheikh, A.A. and Mohamed, H.A. (2013). Calibration estimation in stratified Sampling. The 48th Annual Conference on Statistics, Computer Sciences and Operation Research, Institute of Statistical Studies and Research, Cairo University, Egypt.

7- Hansen, M.H. and Hurwitz, W.N. (1943). On the theory of sampling from finite populations, Annals of Mathmatical Statistic. 14,333-362.

8- Housila, P. S. and Gajendra, K. V. (2007). Modified exponential ratio and product estimators for finite population mean in double sampling, Austrian Journal of Statistics , 36(3), 217–225.

9- Housila, P. S. and Ramkrishna, S. S. (2011). Generalized ratio and product methods of estimation in survey sampling. Pakistan Journal of Statistics and Operation Research, 7(2), 245-264.

10-Jozani, M.J. and Johnson, B.C., (2011). Design based estimation for ranked set sampling in finite populations. Environmental and ecological statistics, 18, 663–685.

11- Kadilar, C. and Cingi, H. (2003). Ratio estimators in stratified random sampling. Biometrical Journal, 45(2), 218-225

12- Kadilar, C. Unyazici, Y. and • Cingi, H. (2009). Ratio estimator for the population mean using ranked set sampling. Statistical Papers, 50,301–309.

13-Kim, J.M. Sungur, E.A and Heo, T-Y. (2006). Calibration approach estimators in stratified sampling. Statistics and Probability Letters, 77, 99–103.

14- Koyuncu, N., and Kadilar. C.(2010). On the family of estimators of population mean in stratified random sampling. Pakistan Journal of Statistics, 26(2), 427-443.

15- Luengo, V.G. (2016). Ratio-cum-product estimation in presence of non-response in successive sampling. Journal of Applied Mathematics, Statistics and Informatics, 12(1), 55-83.

16-Okafor, F.C., and Lee, H., (2000). Double sampling for ratio and regression estimation with subsampling the nonrespondents. Survey Methodology, Statistics Canada, 26(2), 183-188.

17- Prasad, B. (1989). Some improved ratio type estimators of population mean and ratio in finite population sample surveys. Communications in Statistics-Theory and Methods, 18(1), 379-392.

18- Rodriguez, A., Eva, M. , Luengo, G. and Amelia. V. (2001). Estimation of current population ratio in successive sampling. Jour. Ind. Soc. Ag. Statistics, 54(3), 342-354.

19-Samawi, H.M, and Muttlak, H.A. (1996). Estimation of ratio using rank set sampling, Biometrical Journal, 38(6), 753-764.

20- Shahzad, U., Hanif, M., Koyuncu, N. and Luengo,. A.V.G., (2019). A Family of ratio estimators in stratified random sampling utilizing auxiliary attribute alongside the nonresponse issue, Journal of Statistical Theory and Applications, 18(1), 12–25.

21-Singh, S., Horn, S., Yu, F., (1998). Estimation of variance of the general regression estimator: higher level calibration approach. Survey Methodology, 24(1), 41–50.

22-Singh, H.P. and Kakran, M.S. (1993). A modified ratio estimator using known coefficient of kurtosis of an auxiliary character. Revised Version submitted to Journal of Indian Society of Agricultural Statistics, New Delhi, Endia

23-Singh, R., Kumar, M., Singh, R.D., and Chaudhary, M.K. (2008). Exponential ratio type estimators in stratified random sampling, Presented in International Symposium on Optimisation and Statistics (I.S.O.S) at A.M.U., Aligarh, India.

24-Singh, H. P., and Solanki, R. S. (2011). Generalized ratio and product methods of estimation in survey sampling, Pakistan Journal of Statistics and Operation Research, 7(2), 305-314.

25-Sisodia, B.V.S. and Dwivedi, V.K., (1981). A modified ratio estimator using coefficient of variation of auxiliary variable. J. Indian Soc. Agricultural Statist. 33, 13–18.

26- Sriven, T. and Tracy, D.S. (1979). On ratio and product methods of estimation in sampling. Statistica Neerlandica, 33(1), 37-49.

27- Swain, A. K. P. C. (2013). On some modified ratio And product type estimators. Revisted Revista Investgation Operacional , 34(1), 35-57.

28-Upadhyaya, L.N., Singh, H.P., (1999). Use of transformed auxiliary variable in estimating the finite population mean. Biometrical journal. 41,627–636.

29-Wu,C.F.J (1985). Variance Estimation for the combined ratio and combined regression estimators. Royal Statistical Society. 47(1), 147-154.

30-Zaizai,Y. (2006), Ratio method of estimation of population proportion using randomized response technique , Model Assisted Statistics and Applications, 1(2), 125-130.

Published

2020-10-08

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*Journal of Progressive Research in Mathematics*,

*16*(4), 3199-3205. Retrieved from http://www.scitecresearch.com/journals/index.php/jprm/article/view/1924

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