Two classes of GRBs have been confidently identified thus far and are prescribed to different physical scenarios – NS-NS or NS-BH mergers, and collapse of massive stars, for short and long GRBs, respectively. A third, intermediate in duration class, was suggested to be present in previous catalogs, such as BATSE and Swift, based on statistical tests regarding a mixture of two or three log-normal distributions of T_{90}. However, this might possibly not be an adequate model. This paper investigates whether the distributions of log T_{90} from BATSE, Swift, and Fermi are described better by a mixture of skewed distributions rather than standard Gaussians. Mixtures of standard normal, skew-normal, sinh-arcsinh and alpha-skew-normal distributions are fitted using a maximum likelihood method. The preferred model is chosen based on the Akaike information criterion. It is found that mixtures of two skew-normal or two sinh-arcsinh distributions are more likely to describe the observed duration distribution of Fermi than a mixture of three standard Gaussians, and that mixtures of two sinh-arcsinh or two skew-normal distributions are models competing with the conventional three-Gaussian in the case of BATSE and Swift. Based on statistical reasoning, and it is shown that other phenomenological models may describe the observed Fermi, BATSE, and Swift duration distributions at least as well as a mixture of standard normal distributions, and the existence of a third (intermediate) class of GRBs in Fermi data is rejected.