I am working on a paper, and have a problem regarding ellipsoid and Trivariate Normal Distribution. Suprisingly I can't find much in literature but I found your in one of your answers : ''Because this construction has nothing to do with "confidence" per se, the objective is to establish some convention for describing the shape and relative size of the points. Using 1.96 sort of works (for three variables): it contains about 72% of the probability of the trivariate normal distribution. But as the number of variables increases this method produces ellipses that are far too small. For instance, with 10 variables it will contain only 4.6% of the probability; using 4.28 instead of 1.96 in this case will contain 95% of the probability''.
Because this construction has nothing to do with "confidence" per se, the objective is to establish some convention for describing the shape and relative size of the points. Using 1.96 sort of works (for three variables): it contains about 72% of the probability of the trivariate normal distribution. But as the number of variables increases this method produces ellipses that are far too small. For instance, with 10 variables it will contain only 4.6% of the probability; using 4.28 instead of 1.96 in this case will contain 95% of the probability.
How did you get this number 72%? Or do you have some literature to recommend to me in which I can find this. I would appreciate it very much!
