Calibration of the distance scale from galactic Cepheids -: I.: Calibration based on the GFG sample

New estimates of the distances of 36 nearby galaxies are presented based on accurate distances of galactic Cepheids obtained by Gieren et al. (1998) from the geometrical Barnes-Evans method. The concept of "sosie" is applied to extend the distance determination to extragalactic Cepheids without assuming the linearity of the PL relation. Doing so, the distance moduli are obtained in a straightforward way. The correction for extinction is made using two photometric bands (V and I) according to the principles introduced by Freedman & Madore (1990). Finally, the statistical bias due to the incompleteness of the sample is corrected according to the precepts introduced by Teerikorpi (1987) without introducing any free parameters (except the distance modulus itself in an iterative scheme). The final distance moduli depend on the adopted extinction ratio R-V/R-I and on the limiting apparent magnitude of the sample. A comparison with the distance moduli recently published by the Hubble Space Telescope Key Project (HSTKP) team reveals a fair agreement when the same ratio R-V/R-I is used but shows a small discrepancy at large distance. In order to bypass the uncertainty due to the metallicity effect it is suggested to consider only galaxies having nearly the same metallicity as the calibrating Cepheids (i.e. Solar metallicity). The internal uncertainty of the distances is about 0.1 mag but the total uncertainty may reach 0.3 mag.