Ijaz IQBAL, Javid SHABBIR, M.H. TAHIR

Polygonal designs with block size 3 and single distance

Polygonal designs, a class of partially balanced incomplete block de- signs with regular polygons, are useful in survey sampling in terms of balanced sampling plans excluding contiguous units (BSECs) when neighboring units in a population provide similar information. In this paper, the method of cyclic shifts is used to construct cyclic polygonal designs (in terms of BSECs) with block size k = 3 for single distance, and a complete solution for v ∈ {9, 10, . . . , 100} treatments is compiled.

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[1] Bhattacharyya, G., Hegeman, J., Kim, J., Langford, J. and Song, S.Y. Some existence and construction results of polygonal designs, European Journal of Combinatorics 29, 1396–1407, 2008.
[2] Christman, M.C. Efficiency of some sampling designs for spatially clustered populations, Environmetrics 8, 145–166, 1997.
[3] Colbourn, C. J. and Ling, A.C.H. A class of triple systems with applications in survey sampling, Communications in Statistics–Theory and Methods 27, 1009–1018, 1998.
[4] Frank, D.C. and O’Shughnessy, C.D. Polygonal designs, Canadian Journal of Statistics 2, 45–59, 1974.
[5] Hedayat, A. S., Rao, C.R. and Stufken, J. Sampling plans excluding contiguous units, Jour- nal of Statistical Planning and Inference 19, 159–170, 1988.
[6] Hedayat, A. S., Rao, C.R. and Stufken, J. Designs in Survey Sampling Avoiding Contiguous Units, (eds.) P.R. Krishnaiah, C.R. Rao, Handbook of Statistics 6: Sampling (Elsevier, Amsterdam, 1988) 575–583.
[7] Iqbal, I., Tahir, M.H., Akhtar, M., Ghazali, S. S.A., Shabbir, J. and Bukhari, N. S. Gen- eralized polygonal designs with block size 3 and = 1, Journal of Statistical Planning and Inference 139, 3200–3219, 2009.
[8] Mandal, B.N., Parsad R. and Gupta, V.K. Computer-aided construction of balanced sam- pling plans excluding contiguous units, Journal of Statistics and Applications 3, 67–93, 2008.
[9] Mandal, B.N., Parsad, R., Gupta, V.K. and Sud, U.C. A family of distance balanced sampling plans, Journal of Statistical Planning and Inference 139, 860–874, 2009.
[10] See, K. and Song, S.Y. Spatially constrained sampling. In: A.H.El-Shaarwi and W.W. Piegorsch (eds.), Encyclopedia of Environmetrics 4 Wiley, 2080–2083, 2002.
[11] See, K., Song, S.Y. and Stufken J. On a class of partially incomplete block designs with applications in survey sampling, Communications in Statistics–Theory and Methods 26, 1–13, 1997.
[12] See, K., Song, S.Y., Stufken, J. and Bailer, A. J. Relative efficiencies of sampling plans for selecting a small number of units from a rectangular region, Journal of Statistical Compu- tation and Simulation 66, 273–294, 2000.
[13] Stufken, J. Combinatorial and statistical aspects of sampling plans to avoid the selection of adjacent units, Journal of Combinatorial and Information System Sciences 18, 149–160, 1993.
[14] Stufken, J. and Wright, J.H. Polygonal designs with blocks of size k 10, Metrika 54, 179–184, 2001.
[15] Stufken, J., Song, S.Y., See, K. and Driessel, K.R. Polygonal designs: Some existence and non-existence results, Journal of Statistical Planning and Inference 77, 155–166, 1999.
[16] Wei, R. Cyclic BSEC of block size 3, Discrete Mathematics 250, 291–298, 2002.
[17] Zhang, J. and Chang, Y. The spectrum of cyclic BSEC with block size three, Discrete Mathematics 305, 312–322, 2005.