Statistical image reconstruction (SR) algorithms have the potential to significantly reduce x-ray CT image artefacts because they use a more accurate model than conventional filtered backprojection and can incorporate effects such as noise, incomplete data and nonlinear detector response. Most SR algorithms assume that the CT detectors are photon-counting devices and generate Poisson-distributed signals. However, actual CT detectors integrate energy from the x-ray beam and exhibit compound Poisson-distributed signal statistics. This study presents the first assessment of the impact on image quality of the resultant mismatch between the detector and signal statistics models assumed by the sinogram data model and the reconstruction algorithm. A 2D CT projection simulator was created to generate synthetic polyenergetic transmission data assuming (i) photon-counting with simple Poisson-distributed signals and (ii) energy-weighted detection with compound Poisson-distributed signals. An alternating minimization (AM) algorithm was used to reconstruct images from the data models (i) and (ii) for a typical abdominal scan protocol with incident particle fluence levels ranging from 10(5) to 1.6 x 10(6) photons/detector. The images reconstructed from data models (i) and (ii) were compared by visual inspection and image-quality figures of merit. The reconstructed image quality degraded significantly when the means were mismatched from the assumed model. However, if the signal means are appropriately modified, images from data models (i) and (ii) did not differ significantly even when SNR is very low. While data-mean mismatches characteristic of the difference between particle-fluence and energy-fluence transmission can cause significant streaking and cupping artefacts, the mismatch between the actual and assumed CT detector signal statistics did not significantly degrade image quality once systematic data means mismatches were corrected.