Tolerance regions for a multivariate normal population

@article{Slotani1964ToleranceRF,
  title={Tolerance regions for a multivariate normal population},
  author={Mlnoru Slotani},
  journal={Annals of the Institute of Statistical Mathematics},
  year={1964},
  volume={16},
  pages={135-153}
}
  • Mlnoru Slotani
  • Published 1 December 1964
  • Mathematics
  • Annals of the Institute of Statistical Mathematics
A(S) represents the proportion of the population which R(S) includes for a particular sample S. This proportion varies from sample to sample. The requirement (3) for the tolerance region is to guarantee, with the confidence coefficient r, that the proportion A(S) is greater than or equal to a preassigned p. Since we are concerned with a normal population, i t is natural to consider, as R(S), the ellipsoidal region, because the equiprobability surface of the multivariate normal distribution (1… 

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References

SHOWING 1-10 OF 16 REFERENCES

Confidence Bounds on Vector Analogues of the "Ratio of Means" and the "Ratio of Variances" for Two Correlated Normal Variates and Some Associated Tests

1. Summary and Introduction. In this paper coiifidence bounds are obtained (i) on the ratio of variances of a (possibly) correlated bivariate normal population, and then, by generalization, (ii) on a

Tables of the Incomplete Gamma-Function

I SHOULD be greatly obliged if you could allow me a little of your valuable space to state that Dr. J. F. Tocher has kindly pointed out an error in my Introduction to the above Tables. In a table on

Some Aspects of Multivariate Analysis.

Tests of Multiple Independence and the Associated Confidence Bounds

1. Summary. In this paper a test based on the union-intersection principle is proposed for overall independence between p variates distributed according to the multivariate normal law, and this is

Some Further Results in Simultaneous Confidence Interval Estimation

Simultaneous Confidence Interval Estimation