  In high Energy Physics, it is common to look for a localized deviation in
data with respect to a given reference. For this task, the well known
BumpHunter algorithm allows for a model-independent deviation search with the
advantage of estimating a global p-value to account for the Look Elsewhere
Effect. However, this method relies on the generation and scan of thousands of
pseudo-data histograms sampled from the reference background. Thus, accurately
calculating a global significance of $5\sigma$ requires a lot of computing
resources. In order to speed this process and improve the algorithm, we propose
in this paper a solution to estimate the global p-value using a more reasonable
number of pseudo-data histograms. This method uses a functional form inspired
by similar statistical problems to fit the test statistic distribution. We have
found that this alternative method allows to evaluate the global significance
with a precision about 5% up to the $5\sigma$ discovery threshold.
