Cash (ApJ 228, 939) showed that the 
minimization
criterion is a very bad one if any of the observed data bins
had few counts. A better criterion is to use a likelihood function :
where 
are the observed data and 
the values of the function.
Minimizing C for some model gives the best-fit parameters.
Furthermore, this statistic can be used in the same, familiar way as the statistic
to find confidence intervals. One finds the parameter values that give
, where N is the same number that gives the required confidence
for the number of interesting parameters as for the case.
A couple of caveats are in order. The C statistic provides an excellent method
of finding the best-fit parameters and confidence intervals for a model, but it
does not give any measure of how good the fit is (unlike , which does
both for satisfactory data). A goodness-of-fit criterion must be derived using
simulations
. Secondly, the
C-statistic assumes that the error on the counts is
pure Poisson, and thus it cannot deal with data that already has been background
subtracted, or has systematic errors.