Journals / Hacettepe Journal of Mathematics and Statistics / 2012 / Cilt: 41 - Sayı: 4

Polygonal designs with block size 3 and single distance

Pages
587–604
Publication Date
2022-10-18
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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.

📌 3 Key Takeaways

🎯
Objective & Hypothesis: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.
📊
Key Findings & Data: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.
💡
Conclusion & Impact: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.
🔬Design:Survey & Empirical Study
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

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.

🔖

Cite This Article

IQBAL, I., SHABBIR, J., TAHIR, M. (2022). Polygonal designs with block size 3 and single distance. Hacettepe Journal of Mathematics and Statistics, Cilt: 41 - Sayı: 4, 587–604. https://ajindex.com/articles/530529

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  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 an