Additional Details for Robust Normal Mixtures

For the Robust Normal Mixtures method, JMP computes estimates via maximum likelihood with respect to a mixture of Huberized normal distributions. This is a class of modified normal distributions that was developed to be more outlier resistant than the normal distribution.

The Huberized Gaussian distribution has pdf

So, in the limit as k becomes arbitrarily large,

tends toward the normal PDF. As

tends toward the exponential (Laplace) distribution.

The regularization parameter k is set so that P(Normal(x) < k) = Huber Coverage, where Normal(x) indicates a multivariate normal variate. Huber Coverage is a user field, which defaults to 0.90.