A detailed statistical characterization of an optical signal obtained from a heralded single photon source is performed. The source is based on the spontaneous four-wave mixing process, and a dispersion shifted fiber is used to achieve phase matching. At source output, the derivation of the second-order coherence function shows the importance of choosing carefully the frequency detuning between the optical fields in order to avoid the uncorrelated photons generated through Raman scattering. Results indicate that with an accurate adjustment of the source parameters, it is possible to obtain an almost perfect conditional single photon source using spontaneous four-wave mixing. When a transmission fiber is considered, the losses change the source statistics due to the coupling with the noise absorption reservoir. Nevertheless, even at room temperature the impact of the absorption reservoir tends to be quite small, and the change is only observable for very long transmission lengths.