[R] Mahalanobis distance and probability of group membership using Hotelling's T2 distribution

I want to calculate the probability that a group will include a particular point using the squared Mahalanobis distance to the centroid. I understand that the squared Mahalanobis distance is distributed as chi-squared but that for a small number of random samples from a multivariate normal

[R] Mahalanobis distance and probability of group membership using Hotelling's T2 distribution

I want to calculate the probability that a group will include a particular point using the squared Mahalanobis distance to the centroid. I understand that the squared Mahalanobis distance is distributed as chi-squared but that for a small number of random samples from a multivariate normal