  We obtain an approximate Gaussian distribution from a Poisson distribution
after doing a change of variable. A new chi-square function is obtained which
can be used for parameter estimations and goodness-of-fit testing when
adjusting curves to histograms. Since the new distribution is approximately
Gaussian we can use it even when the bin contents are small. The corresponding
chi-square function can be used for curve fitting. This chi-square function is
simple to implement and presents a fast convergence of the parameters to the
correct value, especially for the parameters associated with the width of the
fitted curve. We present a Monte Carlo comparative study of the fitting method
introduced here and two other methods for three types of curves: Gaussian,
Breit-Wigner and Moyal, when each bin content obeys a Poisson distribution. It
is also shown that the new method and the other two converge to the same result
when the number of events increases
