A Central Tolerance Region for the Multivariate Normal Distribution
S. John · Journal of the Royal Statistical Society Series B (Statistical Methodology) · 1968
Summary In a multivariate normal distribution the probability density takes any particular value at all points on the surface of an ellipsoid whose centre is the mean of the distribution. Among such ellipsoids there is one, R, say, that contains 100α per cent of the individuals in the population. The paper deals with the problem of determining from a random sample a region which contains R with prescribed probability β. In the univariate case, R reduces to an interval with the mean as midpoint. Any linear function of variables whose joint distribution is normal has again a normal distribution. Let Ta denote the interval corresponding to R in the case of the linear combination with coefficients vector a. A method of determining from the sample intervals which simultaneously include Ta for all a with probability β is indicated.