Comparison of approximation methods for computing tolerance factors for a multivariate normal population

Technometrics

Volumn 41, Issue 3, 1999, Pages 234-249

  Krishnamoorthy, K ^a   Mathew, Thomas ^b  

^a UNIVERSITY OF LOUISIANA AT LAFAYETTE   (United States)

^b UNIVERSITY OF MARYLAND BALTIMORE COUNTY   (United States)

Author keywords

Chi squared approximation; Noncentral chi squared distribution; Wishart distribution

Indexed keywords

EIGENVALUES AND EIGENFUNCTIONS; FITS AND TOLERANCES; MATRIX ALGEBRA; MONTE CARLO METHODS; NUMERICAL METHODS; PROBABILITY;

CHI SQUARED APPROXIMATION; MULTIVARIATE NORMAL POPULATION; NONCENTRAL CHI SQUARED DISTRIBUTION; TOLERANCE FACTORS; WISHART DISTRIBUTION;

APPROXIMATION THEORY;

EID: 0032643956     PISSN: 00401706     EISSN: 15372723     Source Type: Journal    
DOI: 10.1080/00401706.1999.10485672     Document Type: Article

References (18)

1. Anderson, T. W. (1984), An Introduction to Multivariate Statistical Analysis (2nd ed.), New York: Wiley.
2. Chew, V. (1966), “Confidence, Prediction, and Tolerance Regions for the Multivariate Normal Distribution,” Journal of the American Statistical Association, 61, 605-617.
3. Eberhardt, K. R., Mee, R. W., and Reeve, C. P. (1989), “Computing Factors for Exact Two-Sided Tolerance Intervals for a Normal Distribution,” Communications in Statistics-Simulation and Computation, 18, 397-413.
4. Fuchs, C., and Kenett, R. S. (1987), “Multivariate Tolerance Regions and F-Tests,” Journal of Quality Technology, 19, 122-131.
5. Fuchs, C., and Kenett, R. S. (1988), “Appraisal of Ceramic Substrates by Multivariate Tolerance Regions,” The Statistician, 37, 401-411.
6. Guttman, I. (1970a), Statistical Tolerance Regions, Classical and Bayesian, London: Griffin’s Statistical Monographs.
7. Guttman, I. (1970b), “Construction of /3-Content Tolerance Regions at Confidence Level 7 for Large Samples From the fc-Variate Normal Distribution,” The Annals of Mathematical Statistics, 41, 376-400.
8. Hall, I. J., and Sheldon, D. D. (1979), “Improved Bivariate Normal Tolerance Regions With Some Applications,” Journal of Quality Technology, 11, 13-19.
9. Hoel, P. G. (1937), “A Significance Test for Component Analysis,” The Annals of Mathematical Statistics, 8, 149-158.
10. John, S. (1963), “A Tolerance Region for Multivariate Normal Distributions,” Sankhya, Ser. A, 25, 363-368.
11. Kendall, M. G., and Stuart, A. (1973), The Advanced Theory of Statistics, Vol. 2, New York: Hafner.
12. Muirhead, R. J. (1982), Aspects of Multivariate Statistical Theory, New York: Wiley.
13. Rao, C. R. (1973), Linear Statistical Inference and Its Applications (2nd ed.), New York: Wiley.
14. Siotani, M. (1964), “Tolerance Regions for a Multivariate Normal Population,” Annals of the Institute of Statistical Mathematics, 16, 135-153.
15. Smith, W. B., and Hocking, R. R. (1972), “Wishart Variates Generator (algorithm AS 53),” Applied Statistics, 21, 341-345.
16. von Rosen, D. (1988), “Moments for the Inverted Wishart Distribution,” Scandinavian Journal of Statistics, 15, 97-109.
17. Wald, A. (1942), “Setting of Tolerance Limits When the Sample is Large,” The Annals of Mathematical Statistics, 13, 389-399.
18. Wald, A., and Wolfowitz, J. (1946), “Tolerance Limits for a Normal Distribution,” The Annals of Mathematical Statistics, 17, 208-215.