An asymptotic result on principal points for univariate distributions
Klaus Pötzelberger, K. Felsenstein · Optimization · 1994
We give an asymptotic result for principal points of univariate distributions, as defined in Flury (1990). Principal points are a generalization of the mean and provide a natural way to approximate a continuous distribution. We show that for a given density $si:f$esi:it is asymptotically optimal to take the quantiles of the density proportional to$si:f$esi:i1/3 as principal points.