Context : The Initial Mass Function ( IMF ) plays a crucial role on galaxy evolution and its implications on star formation theory make it a milestone for the next decade .
It is in the intermediate and high mass ranges where the uncertainties of the IMF are larger .
This is a major subject of debate and analysis both for Galactic and extragalactic science .

Aims : Our goal is to constrain the IMF of the Galactic thin disc population using both Galactic Classical Cepheids and Tycho-2 data .

Methods : For the first time the Besançon Galaxy Model ( BGM ) has been used to characterise the Galactic population of the Classical Cepheids .
We have modified the age configuration in the youngest populations of the BGM thin disc model to avoid artificial discontinuities in the age distribution of the simulated Cepheids .
Three statistical methods , optimized for different mass ranges , have been developed and applied to search for the best IMF that fits the observations .
This strategy allows us to quantify variations in the Star Formation History ( SFH ) , the stellar density at Sun position and the thin disc radial scale length .
A rigorous treatment of unresolved multiple stellar systems has been undertaken adopting a spatial resolution according to the catalogues used .

Results : For intermediate masses , our study favours a composite field-star IMF slope of \alpha = 3.2 for the local thin disc , excluding flatter values such as the Salpeter IMF ( \alpha = 2.35 ) .
Our findings are broadly consistent with previous results derived from Milky Way models .
Moreover , a constant Star Formation History is definitively excluded , the three statistical methods considered here show that it is inconsistent with the observational data .

Conclusions : Using field stars and Galactic Classical Cepheids , we have found , above 1 M _ { \odot } , an IMF steeper than the canonical stellar IMF of associations and young clusters .
This result is consistent with the predictions of the Integrated Galactic IMF .