The photon counting histogram (PCH) analysis of the fluorescence fluctuations provides the molecular brightness (epsilon) and the average number of fluorophores (N) in an open observation volume. PCH, which is based on the analysis of the whole of the photon counting histogram, has been recently improved by taking into account the detector dead time effect, which is relevant at high fluorescence rates. We investigate here the possibility of quantitatively applying the PCH analysis in the simplified form of photon moment analysis, in which only the first two moments of the photon counting histogram are computed. We have applied this analysis to low fluorescence signals from living cells in the presence of cell micro-movements and molecular photo-bleaching and describe a simple algorithm for its routine application. The algorithm has been tested on Saccharomyces Cerevisiae (yeast) cells labeled with Dimethyl-pepep and Rhodamine 6G, and Chinese Hamster Ovary (CHO) cells stably expressing the regulatory subunit (RII) of protein kinase A fused to the cyan-emitting variant of GFP (CFP). Our statistical analysis allows us to estimate the local concentrations and the brightness of the fluorophores in different cellular compartments (nucleus, membrane, and cytoplasm) despite the occurrence of microscopic cell movements and significant photo-bleaching.