A method and apparatus for determining a parameter vector that includes a plurality of parameters of a detector pileup model of a photon-counting detector, the detector pileup model being used for pileup correction for a spectral computed-tomography scanner. The method includes setting values of the parameters, the parameters including a dead time parameter and individual probabilities of different pileup events, the probabilities including a probability of single photon events, a probability of double quasi-coincident photon events, and a probability of at least three quasi-coincident photon events. The method include determining, using (1) a detector response model, (2) an incident spectrum, and (3) the set values of the parameter vector, a plurality of component spectra, each component spectrum corresponding to one of the individual probabilities of the different pileup events, and summing the plurality of component spectra to generate an output spectrum.