# 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} }

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…

## 59 Citations

Tolerance regions in multivariate linear regression

- Mathematics
- 2004

Abstract The construction of tolerance regions is investigated for a multivariate linear regression model under the multivariate normality assumption. In the context of such a model, a tolerance…

Moments of coverage of a random ellipsoid

- Mathematics
- 1986

SummaryExact expressions are obtained for the moments of coverage of the random ellipsoid
$$T_r (\bar x,S(X)) = \{ y|(y - \bar x)'S^{ - 1} (X)(y - \bar x) \leqq r\}$$
whereX=p1,...,pn is a sample…

Improved Tolerance Factors for Multivariate Normal Distributions

- Mathematics
- 2006

ABSTRACT In this article, an improved method of computing tolerance factors for multivariate normal distributions is proposed. The method involves an approximation and simulation, and is more…

Comparison of Approximation Methods for Computing Tolerance Factors for a Multivariate Normal Population

- Computer ScienceTechnometrics
- 1999

This article compares several approximation methods for computing the tolerance factors of a multivariate normal population and suggests some new approximations, which give satisfactory results and provide guidelines regarding the choice of the tolerance factor for practical applications.

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

- Mathematics
- 1999

In this article, we compare several approximation methods for computing the tolerance factors of a multivariate normal population. These approximate methods are evaluated by comparing the Monte Carlo…

Multivariate Analysis Improved Tolerance Factors for Multivariate Normal Distributions

- Mathematics
- 2006

In this article, an improved method of computing tolerance factors for multivariate normal distributions is proposed. The method involves an approximation and simulation, and is more accurate than…

Survey of Properties and Applications of the Noncentral t-Distribution

- Mathematics
- 1968

Applications are outlined of the noncentral t-distribution to tolerance limits, to variables sampling plans, to confidence limits on a quantile, to confidence limits on a proportion, to the…

Central tolerance regions and reference regions for multivariate normal populations

- Computer Science, MathematicsJ. Multivar. Anal.
- 2015

The construction of a central tolerance region is investigated for a multivariate normal population, and also for aMultivariate normal linear regression model, and a theoretical framework is developed that will facilitate the numerical computation of the tolerance factor.

Tolerance limits for the p-dimensional radial error distribution

- Mathematics
- 1974

Tolerance limits are formulated for the p-dimensional radial error distribution. The limits are of the form where k is the tolerance limit factor and is the maximum likelihood estimator for the…

Confidence, Prediction, and Tolerance Regions for the Multivariate Normal Distribution

- Mathematics
- 1966

Abstract Formulas for confidence, prediction, and tolerance regions for the multivariate normal distribution for the various cases of known and unknown mean vector and covariance matrix are assembled…

## 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

- Mathematics
- 1958

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…

Tests of Multiple Independence and the Associated Confidence Bounds

- Mathematics
- 1958

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…

Tables of the Incomplete Gamma-Function

- MathematicsNature
- 1922

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…