In high energy physics, the most frequently encountered standard
distributions governing frequencies (e.g. for events) are the
Poisson distribution, the Gaussian distribution, and the
binomial distribution. The statistical literature is replete
with excellent discussions of these and other distributions, and
a full explication will not be given here. (See the statistics
books and statistics reference section of this site.) However,
here a few rules of thumb and guidelines are in order: One of
the most frequently occurring problems in high-energy physics is
to compare an observed distribution with a prediction, for
example from a simulation. Indeed, an analysis might be designed
to extract some physical parameter from the simulation or
prediction which best fits the data. (See also the page on
goodness of fit tests.) For data points with Gaussian errors,
one can write a chi square function Here the yi are the observed
data, and the yi with ~'s are the predictions of the model at
each point. The chi square expr