  We propose an approach considering the nonextensive effects in the context of
the Verlinde theory in order to address an extended cosmological model in the
context of viscous dark energy. Specifically, this model leads to a tiny
perturbation in the dynamics of the expansion of the universe through the
generalized Friedmann equations so-called the extended $\Lambda$CDM model. From
the observational test standpoint, we make a Bayesian analysis of the models of
bulk viscosity for dark energy which follows the Eckart theory of bulk
viscosity. These models are investigated through the context of both models
$\Lambda$CDM and extended $\Lambda$CDM. The Bayesian analysis is performed
using the data of CMB Distance priors, Baryon Acoustic Oscillations
Measurements, Cosmic Chronometers, and SNe Ia distance measurements.
