  In this work, we try to improve the classic asymptotic formulae to describe
the probability distribution of likelihood-ratio statistical tests. The idea is
to split the probability distribution function into two parts. One part is
universal and described by the asymptotic formulae. The other part is
case-dependent and estimated explicitly using a 6-bin model proposed in this
work. The latter is similar to doing toy simulations and hence is able to
predict the discrete structures in the probability distributions. The new
asymptotic formulae provide a much better differential description of the test
statistics. The better performance is confirmed in two toy examples.
