  Microarray data come from many steps of production and have been known to
contain noise. The pre-processing is implemented to reduce the noise, where the
background is corrected. Prior to further analysis, many Illumina BeadArrays
users had applied the convolution model, a model which had been adapted from
when it was first developed on the Affymetrix platform, to adjust the intensity
value: corrected background intensity value.
  Several models based on different underlying distributions and or parameters
estimation methods have been proposed and applied. For instance : the
exponential-gamma, the normal-gamma and the exponential-normal convolutions
with a maximum likelihood estimation, non-parametric, Bayesian and moment
methods of the parameters estimation, including two recent
exponential-lognormal and gamma-lognormal convolutions.
  In this paper, we propose models and derive the corrected background
intensity based on the generalized betas and the generalized beta-normal
convolutions as a generalization of the existing models.
