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Photoionization models usually assume Maxwell\u2013Boltzmann (M\u2013B) electron energy distributions (EED), but it has been suggested that using \u03ba distributions may be more appropriate and could potentially solve the discrepancies in temperatures and abundances found in HII regions and planetary nebulae. We consider the impact of the presence of \u03ba distributions in photoionized nebulae associated with AGN and study how this might affect spectral modelling and abundance analyses for such regions. Using the photoionization code MAPPINGS 1e, we compute models adopting M\u2013B and \u03ba distributions of electron energies and compare the behaviour of emission line ratios for different values of \u03ba, gas metallicity, density, ionization parameter, and SED slope. We find that the choice of EED can have a large impact on some UV and optical emission lines emitted by photoionized nebulae associated with AGN, and that the impact of adopting a \u03ba distribution is strongly dependent on gas metallicity and ionization parameter. We compile a sample of line ratios for 143 type 2 AGN and compare our models against the observed line ratios. We find that for 98 objects, \u03ba distributions provide a better fit to the observed line ratios than M\u2013B distributions. 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