Characterization of Group Divisible Designs
Abstract:
In this paper, some inequalities of PBIB designs have been given. In this paper, the characterization of all the three types of GD designs, by finding some equalities and inequalities among the parameters of GD designs is obtained.
Author(s):
DOI:
Keywords:
References:
Bhagwandas, Banerjee, S. and Kageyama, S. Patterned constructions of partially balanced incomplete block designs, Journal of Comm. Statist., A 14, 1259- 1267, (1985).
Bose, R.C. and Connor, W.S. Combinatorial properties of group divisible incomplete block designs. Journal of Ann. Math. Statist., 23, 367-383, (1952). http://dx.doi.org/10.1214/aoms/1177729382
Bose, R.C. and Nair, K.R. Partially Balanced Incomplete Block Designs. Sankhya. 4, 307- 372 , (1939).
Bose, R.C. and Shimamoto, T. Classification and Analysis of Partially Balanced Incomplete Block Designs with two Associate Classes, Journal of Amer. Statist. Assoc., 47, 151-184, (1952). http://dx.doi.org/10.1080/01621459.1952.10501161
Clatworthy W. H. Tables of Two-Associates-Class Partially Balanced Designs, NBS Applied Mathematics Series 63, Washington, Dc, (1973).
Dey, A. and Nigam, A.K. Construction of group divisible designs, Journal of Indian soc. Agril. Statist., 37, 163-166, (1985).
Freeman, G.H. Some further methods of constructing regular group divisible incomplete block designs, Journal of Ann. Math. Statist., 28(2), 479-487, (1956) http://dx.doi.org/10.1214/aoms/1177706976.
Ghosh D. K. and Das M. N. Construction of Two Way Group Divisible Designs with Partial Balance for Group Comparisons, Sankhya: The Indian Journal of Statistics, Series B, 55(1), 111-117, (1993).
Ghosh, D. K. and Divecha, Jyoti. Some new semi-regular GD designs, Sankhya, 57, 453-455, (1995).
Kageyama, S. A structural classification of semi-regular group divisible designs, Journal of Statist. and Prob. Letters, 3, 25-27, (1985a). http://dx.doi.org/10.1016/0167-7152(85)90007-0
Kageyama, S. A construction of group divisible designs, Journal of Statist. Plann. and Infer., 12, 123-125, (1985b). http://dx.doi.org/10.1016/0378-3758(85)90060-6
Nair, K. R. and Rao, C. R. A Note on Partially Balanced Incomplete Block Designs, Journal of Science and Culture, 7, 568-569, (1942).
