This paper presents a new modified diagonal systematic sampling method for the linear trend situation. For numerical illustration, data from the literature have been used to compare the proposed method's efficiency with some existing sampling schemes. The findings show that the proposed new systematic sampling method is more efficient than the existing sampling schemes. Moreover, the improvement in efficiency has also been shown in the case of a perfect linear trend. Mathematical conditions under which the new method is more efficient than the existing sampling schemes have been derived.
Citation: Muhammad Azeem, Muhammad Asif, Muhammad Ilyas, Muhammad Rafiq, Shabir Ahmad. An efficient modification to diagonal systematic sampling for finite populations[J]. AIMS Mathematics, 2021, 6(5): 5193-5204. doi: 10.3934/math.2021308
This paper presents a new modified diagonal systematic sampling method for the linear trend situation. For numerical illustration, data from the literature have been used to compare the proposed method's efficiency with some existing sampling schemes. The findings show that the proposed new systematic sampling method is more efficient than the existing sampling schemes. Moreover, the improvement in efficiency has also been shown in the case of a perfect linear trend. Mathematical conditions under which the new method is more efficient than the existing sampling schemes have been derived.
[1] | W. G. Madow, L. H. Madow, On the theory of systematic sampling, I, Ann. Math. Statist., 15 (1944), 1-24. doi: 10.1214/aoms/1177731312 |
[2] | J. Subramani, S. N. Gupta, G. Prabavathy, Circular systematic sampling in the presence of linear trend, Am. J. Math. Manage. Sci., 33 (2014), 1-19. |
[3] | H. J. Chang, K. C. Huang, Remainder linear systematic sampling, Sankhya: Indian J. Stat. Ser. B, 62 (2000), 249-256. |
[4] | J. Subramani, Diagonal systematic sampling scheme for finite populations. J. Indian Soc. Agric. Stat., 53 (2000), 187-195. |
[5] | S. Sampath, V. Varalakshmi, Diagonal circular systematic sampling, Model Assisted Stat. Appl., 3 (2008), 345-352. |
[6] | J. Subramani, Further results on diagonal systematic sampling for finite populations, J. Indian Soc. Agric. Stati., 63 (2009), 277-282. |
[7] | J. Subramani, A modification on linear systematic sampling for odd sample size, Bonfring Int. J. Data Min., 2 (2012), 32-36. doi: 10.9756/BIJDM.1354 |
[8] | J. Subramani, S. N. Gupta, Generalized modified linear systematic sampling scheme for finite populations, Hacet. J. Math. Stat., 43 (2014), 529-542. |
[9] | W. G. Madow, On the theory of systematic sampling Ⅲ-comparison of centered and random start systematic sampling, Ann. Math. Statist., 24 (1953), 101-106. doi: 10.1214/aoms/1177729087 |
[10] | F. Yates, Systematic sampling. Philos. T. R. Soc A, 241 (1948), 345-377. |
[11] | D. R. Bellhouse, J. N. K Raom, Systematic sampling in the presence of linear trends, Biometrika, 62 (1975), 694-697. |
[12] | D. R. Bellhouse, 6 Systematic sampling, Handbook Stat., 6 (1988), 125-145. |
[13] | R. L. Fountain, P. L. Pathak, Systematic and non-random sampling in the presence of linear trends, Commun. Stat-Theory M., 18 (1989), 2511-2526. doi: 10.1080/03610928908830047 |
[14] | S. Sampath, N. Uthayakumaran, Markov systematic sampling, Biometrical J., 40 (1998), 883-895. |
[15] | J. Subramani, A modification on linear systematic sampling, Model Assisted Stat. Appl., 8 (2013), 215-227. |
[16] | D. G. Horvitz, D. J. Thompson, A generalization of sampling without replacement from finite universe, J. Am. Stat. Assoc., 47 (1952), 663-685. doi: 10.1080/01621459.1952.10483446 |
[17] | V. M. Joshi, Note on the admissibility of the sen-yates-grundy variance estimator and murthy's estimator and its variance estimator for samples of size two, Sankhyā: Indian J. Stat. Ser. A, 32 (1970), 431-438. |
[18] | F. Yates, P. M. Grundy, Selection without replacement from within strata with probability proportional to size, J. R. Stat. Soc. Ser. B, 15 (1953), 253-261. |
[19] | T. K. Pandey, V. Kumar, Systematic sampling for non-linear trend in milk yield data, J. Reliab. Stat. Stud., 7 (2014), 157-168. |