A MATHEMATICAL PROGRAMMING APPROACH IN OPTIMUM STRATIFICATION UNDER NEYMAN ALLOCATION FOR TWO STRATIFYING VARIABLES

Authors

  • Faizan Danish Research Consultation Services, Doha, Qatar
  • S.E.H. Rizvi 2,3Division of Statistics and Computer science, Faculty of Basic Sciences, Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, India
  • Manish Kumar Sharma Division of Statistics and Computer science, Faculty of Basic Sciences, Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, India
  • Sudhakar Dwivedi Division of Agricultural Economics and ABM, Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, India
  • Bupesh Kumar Division of Plant Breeding and Genetics, Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, India
  • Sanjeev Kumar Division of Plant Breeding and Genetics ACRA, Dhiansar, Sher-e-Kashmir University of Agricultural Sciences and Technology of Jammu, India

DOI:

https://doi.org/10.13052/jrss2229-5666.12213

Keywords:

Optimum Stratification, Dynamic Programming, Auxiliary Information

Abstract

The current study discusses the solution for obtaining stratification points under Neyman allocation having one study variable and two auxiliary variables. Using dynamic programming approach non-linear programming problem has been solved. The proposed technique has gained in precision rather than using only one auxiliary variable. Numerical illustration has been given in which each of the auxiliary variable is supposed to follow different distribution. Through the empirical study, the proposed method has been compared with the Ravindra and Sukhatme (1969) and Khan et al.(2005) methods with the conclusion of having its more relative efficiency.

Downloads

Download data is not yet available.

References

Dalenius, T. (1950).The problem of optimum stratification-Ii, Skand. Aktuartidskr, 33, p. 203-213.

Dalenius, T. and Gurney, M. (1951). The problem of optimum stratification-II, Skand. Aktuartidskr, 34, p. 133-148.

Dalenius, T. and Hodges, J. L. (1959). Minimum variance stratification, J. Amer. Statist. Assoc., 54, p. 88-101.

Danish , F. and Rizvi, S.E.H. (2017). On optimum stratification using mathematical programming approach, International Research Journal of Agricultural Economics and Statistics, 8(2), p. 435-439.

Danish, F., Rizvi, S.E.H. Jeelani, M. I and Reashi J.A. (2017a). Obtaining strata boundaries under proportional allocation with varying cost of every unit, Pak. J. Stat. Oper. Res., 13(3), p. 567-574.

Danish, F., Rizvi, S.E.H. Jeelani, Sharma, M.K. and M. I.J (2017b). Optimum stratification using mathematical programming approach: a review, Stat. Appl. Prob. Lett. , 4(3), p. 123-129.

Fanolahi, A.V. and Khan, M.G.M. (2014).Determining the optimum strata boundaries with constant cost factor, Conference: IEEE Asia Pacific World Congress on Computer Science And Engineering (Apwc), At Plantation Island, Fiji.

Khan, M.G.M. , Khan, E.A. and Ahsan , M.J. (2003). An optimal multivariate stratified sampling design using dynamic programming, Aust. N. Z. J. Stat, 45(1), p.107–113.

Khan, M. G. M., Najmussehar and Ahsan, M. J. (2005). Optimum stratification for exponential study variable under neyman allocation, J. Indian Soc. Agricultural Statist., 59(2), p. 146-150.

Khan, M. G. M., Nand, N. and Ahmad,N. (2008). Determining the optimum strata boundary points using dynamic programming, Survey Methodology, 34 (2), p. 205-214.

Khan, M. G. M., Ahmad, N. and Khan, Sabiha (2009). Determining the optimum stratum boundaries using mathematical programming, J. Math. Model. Algorithms, Springer, Netherland, 8(4), p. 409- 423.

Khan, M. G. M. , Rao, D., Ansari, A.H. and Ahsan, M.J. (2015). Determining optimum strata boundaries and sample sizes for skewed population with log- normal distribution, Communication in Statistics –Simulation and Computation, 44, p.1364-1387.

Mahalanobis, P. C. (1952). Some aspects of the design of sample surveys, Sankhya, 12, p. 1-7.

Rao, D., Khan, M.G.M. and Khan, S. (2012). Mathematical programming on multivariate calibration estimation in stratified sampling, World Academy of Science, Engineering and Technology, 6, p. 12-27.

Rao, D.K., Khan, M.G.M. and Reddy, K.G. (2014). Optimum stratification of a skewed population, International Journal of Mathematical, Computational, Natural and Physical Engineering, 8(3), p. 497-500.

Rizvi, S. E. H., Gupta, J. P. and Bhargava, M. (2002). Optimum stratification based on auxiliary variable for compromise allocation, Metron, 28(1), p. 201- 215.

Sebnem, Er.(2011). Computation methods for optmum stratification: an overview. Int.Statistical Inst.:Proc.58th World Stastistical Congress. Dulbin, (Sts 058).

Singh, R. (1971). Approximately optimum stratification on the auxiliary variable, J. Amer. Statist. Assoc., 66, p. 829-833.

Singh, R. (1975). An alternate method of stratification on the auxiliary Variable, Sankhya, 37, p. 100-108.

Singh, R. and Sukhatme, B. V. (1969). Optimum stratification for equal allocation, Ann. Inst. Statist. Math., 27, p. 273-280.

Downloads

Published

2019-12-10

How to Cite

Danish , F. ., Rizvi, S., Sharma, M. K. ., Dwivedi , S. ., Kumar, B. ., & Kumar, S. . (2019). A MATHEMATICAL PROGRAMMING APPROACH IN OPTIMUM STRATIFICATION UNDER NEYMAN ALLOCATION FOR TWO STRATIFYING VARIABLES. Journal of Reliability and Statistical Studies, 12(02), 173–185. https://doi.org/10.13052/jrss2229-5666.12213

Issue

2019: Vol 12 Iss 2

Section

Articles