On Modeling Profiles instead of Values
  We consider the problem of estimating the distribution underlying an observed
sample of data. Instead of maximum likelihood, which maximizes the probability
of the ob served values, we propose a different estimate, the high-profile
distribution, which maximizes the probability of the observed profile the
number of symbols appearing any given number of times. We determine the
high-profile distribution of several data samples, establish some of its
general properties, and show that when the number of distinct symbols observed
is small compared to the data size, the high-profile and maximum-likelihood
distributions are roughly the same, but when the number of symbols is large,
the distributions differ, and high-profile better explains the data.
