High Precision Numerical Computation of Principal Points For Univariate Distributions

Principal points were first introduced by Flury: for a positive integer $n$, $n$ principal points of a random variable are the $n$ points that minimize the mean squared distance between the random variable and the nearest of the $n$ points. In this paper, we determine the $n$ principal points and the corresponding values of mean squared distance for different values of $n$ for some univariate absolutely continuous distributions.