GPUs represent one of the most sophisticated and versatile parallel computing architectures that have recently been introduced in the High Energy Physics (HEP) field.
GooFit is an open source tool interfacing ROOT/RooFit to the CUDA platform that allows to manipulate probability density functions and perform fitting tasks. The striking performances and computing capabilities of GPUs, in comparison to traditional CPU cores, have been exploited in the application of a high-statistics pseudo-experiment method implemented in GooFit, with the purpose of estimating the local or global statistical significance of a physics signal, already known or new respectively. When dealing with an unexpected new signal, a global significance must be estimated to take into account the Look-Elsewhere-Effect and this is accomplished coupling a clustering-based scanning technique to the pseudo-experiments method, also without introducing any relevant systematic uncertainty.

By means of these tools it has been possible to investigate the approximation characterizing modern, and currently widely used, statistical methods. In particular two studies have been carried out:
1) the asymptotic behaviour of a likelihood ratio test statistics (Cowan-Cranmer-Gross-Vitells) has been investigated while estimating the local statistical significance of a known signal,
2) the approximation of the Gross-Vitells method (trial factors) has been explored while estimating the global statistical significance of a new signal.

These studies have been collected and presented here coherently with a didactic approach.
Indeed this work is currently used in lectures about Statistics for Data Analysis.
However the presented results can be a useful reference for the confirmation - by means of GPUs - of the validity of few asymptotic formulas/methods now commonly used in HEP.