For what is regarding the BWF functions, which are based on Lorentzian functions, we are here proposing their q-generalized form, that is a form based on the q-Gaussian exponential (to the best of author knowledge, this is the first time a q-BWF function is proposed). However, to substitute the asymmetric pseudo-Voigtian or Voigtian functions, a different form of asymmetric q-Gaussian function exists, and it is that used by S. Devi, 2021, for modeling the financial market dynamics. The asymmetric q-Gaussian is made by two different half q-Gaussians, chosen to fit the two sides of the band.