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Numerical Operations on a Relational Database
May 1989 (vol. 15 no. 5)
pp. 600-610

The problem is discussed of defining numerical operations on a relational database to accommodate the statistical analyses associated with a bivariate frequency table. An attempt has been made to extend Codd's relational algebra to include simple bivariate statistical operations preserving the closure of Codd's algebra. This extended algebra is applied to bivariate relational data structures needed for real-time automatic statistical quality control of a manufacturing process. Also discussed are some new category-numeric operations on relational tables.

[1] R. Agrawal, "Alpha: An Extension of Relational Algebra to Express a Class of Recursive Queries,"Proc. Third Int'l Conf. Data Eng., CS Press, Los Alamitos, Calif., Order No. FN762, 1987, pp. 580-590.
[2] E. F. Codd, "A relational model of data for large shared data banks,"Commun. ACM, pp. 377-387, June 1970.
[3] E. Fortunato, M. Rafanelli, F. L. Ricci, and A. Sebastio, "An algebra for statistical data," inProc. Third Int. Workshop Stat. Sci. Database Management, Luxembourg, July 22-24, 1986, pp. 122-134.
[4] S.P. Ghosh, "An application of statistical databases in manufacturing testing," inProc. COMPDEC, vol. 1, 1984, pp. 96-103.
[5] S.P. Ghosh, "Statistical Relational Tables for Statistical Database Management,"IEEE Trans. on Software Eng., Vol. SE-12, No. 12, Dec. 1986, pp. 1,106- 1.116.
[6] S. P. Ghosh, "Statistics Metadata: Linear Regression Analysis," inFoundations of Data Organization. New York: Plenum, 1987, pp. 3-17; also, IBM Res. Rep. No. RJ 4444, 1984.
[7] S.P. Ghosh, "Statistical data reduction for manufacturing testing," inProc. IEEE Int. Conf. Data Eng., Los Angeles, CA, 1985, pp. 58-66.
[8] S. P. Ghosh, "SIAM: Statistical information access method," IBM Res. Rep. No. 4865, 1985: also, inThird Int. Workshop Stat. Sci. Database Management, Luxembourg, July 22-24, 1986.
[9] S. P. Ghosh,Data Base Organization Jor Data Management, 2nd ed. New York: Academic, 1986.
[10] R. Hammond and J. L. McCarthy, Eds.,Proc. Second Int. Workshop Stat. Database Management, Los Altos, CA, Sept. 27-29, 1983.
[11] A. Klug, "Equivalence of Relational Algebra and Relational Calculus Query Languages Having Aggregate Functions,"J. ACM, Vol. 29, No. 3, July 1982, pp. 699-717.
[12] P. Kreps, "A semantic core model for statistical and scientific data bases," inLBL Perspective on Statistical Database Management, H. K. T. Wong, Ed. Berkeley, CA: Lawrence Berkeley Laboratory, Univ. California, 1982, pp. 129-157.
[13] M. G. Kendall and A. Stuart,The Advanced Theory of Statistics, Vol. 1. London UK: Charles Griffin, ch. 1-6.
[14] M. G. Kendall and A. Stuart,The Advanced Theory of Statistics, Vol. 2. New York: Hafner, 1961, ch. 17-20.
[15] A. Shoshani, "Statistical databases: Characteristics, problems, and some solutions," inProc. 8th Int. Conf. Very Large Data Bases, Mexico City, Mexico, 1982, pp. 208-222.
[16] S. S. Y. W. Su, "SAM*: A semantic association model for corporate and scientific-statistical databases,"J. Inform. Sci., vol. 29, pp. 151- 199, 1983.
[17] SQL/Data System Application Programming, IBM Program Prod. SH24-5018-0, 1983.
[18] M. Stonebraker, Ed.Ingres Papers. Reading, MA: Addison-Wesley, 1986.
[19] H. K. T. Wong, Ed.LBL Perspective on Statistical Database Management. Lawrence Berkeley Laboratory, Univ. California, 1982.
[20] H. K. T. Wong, Ed.Proc. First LBL Workshop Stat. Database Management, Menlo Park, CA, 1982.
[21] J. D. Gibbons,Nonparametric Statistical Inference, 2nd ed. New York: Marcel Dekker, 1985.
[22] M. M. Zloof, "Query by examples," inProc. AFIPS NCC, vol. 44, 1975, pp. 431-438.
[23] SAS User's Guide: Basics, SAS Institute, Cary, NC.
[24] Proc. Third Int. Workshop Stat. Sci. Database Management, Luxembourg, July 22-24, 1986.

Index Terms:
Codd; relational database; numerical operations; statistical analyses; bivariate frequency table; relational algebra; bivariate statistical operations; bivariate relational data structures; real-time automatic statistical quality control; manufacturing process; category-numeric operations; relational tables; database theory; relational databases; statistical analysis
Citation:
S.P. Ghosh, "Numerical Operations on a Relational Database," IEEE Transactions on Software Engineering, vol. 15, no. 5, pp. 600-610, May 1989, doi:10.1109/32.24709
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