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Purpose: Quantification of hypoxia from PET images is of considerable clinical interest. In the absence of dynamic PET imaging the hypoxic fraction (HF) of a tumor has to be estimated from voxel values of activity concentration of a radioactive hypoxia tracer. This work is part of an effort to standardize quantification of tumor hypoxic fraction from PET images. Methods: A simple hypoxia imaging model in the tumor was developed. The distribution of the tracer activity was described as the sum of two different probability distributions, one for the normoxic (and necrotic), the other for the hypoxic voxels. The widths of the distributions arise due to variability of the transport, tumor tissue inhomogeneity, tracer binding kinetics, and due to PET image noise. Quantification of HF was performed for various levels of variability using two different methodologies: a) classification thresholds between normoxic and hypoxic voxels based on a non-hypoxic surrogate (muscle), and b) estimation of the (posterior) probability distributions based on maximizing likelihood optimization that does not require a surrogate. Data from the hypoxia imaging model and from 27 cervical cancer patients enrolled in a FAZA PET study were analyzed. Results: In the model, where the true value of HF is known, thresholds usually underestimate the value for large variability. For the patients, a significant uncertainty of the HF values (an average intra-patient range of 17%) was caused by spatial non-uniformity of image noise which is a hallmark of all PET images. Maximum likelihood estimation (MLE) is able to directly optimize for the weights of both distributions, however, may suffer from poor optimization convergence. For some patients, MLE-based HF values showed significant differences to threshold-based HF-values. Conclusion: HF-values depend critically on the magnitude of the different sources of tracer uptake variability. A measure of confidence should also be reported.