A k-sigma error ellipsoid is defined as a locus of points
In the one dimensional case this is the interval . For any 1D Gaussian
distribution, it is true that approximately 65% of the
occurrences of the random variable are within this range for k=1,
approximately 95% for k=2, approximately 99%
for k=3, etc. Hence, the probability that a Gaussian distribution
will generate a random variable outside this range is approximately
35%, 5%, and 1%, respectively. This
probability is called k-sigma probability and is denoted by P[k].
P[k] can be computed numerically for univariate as well as for
multivariate Gaussian distributions, where it should be noted that
for the same values of k, (here N and (N+1) denote dimensions). For Gaussian
mixture models the k-sigma probability is computed as:
If the parameters are valid, the operator evaluate_class_gmmevaluate_class_gmmEvaluateClassGmmevaluate_class_gmmEvaluateClassGmmEvaluateClassGmm
returns the value 2 (H_MSG_TRUE). If necessary an exception is
Christopher M. Bishop: “Neural Networks for Pattern Recognition”;
Oxford University Press, Oxford; 1995.
Mario A.T. Figueiredo: “Unsupervised Learning of Finite Mixture
Models”; IEEE Transactions on Pattern Analysis and Machine
Intelligence, Vol. 24, No. 3; March 2002.