  The power-law distribution plays a crucial role in complex networks as well
as various applied sciences. Investigating whether the degree distribution of a
network follows a power-law distribution is an important concern. The commonly
used inferential methods for estimating the model parameters often yield biased
estimates, which can lead to the rejection of the hypothesis that a model
conforms to a power-law. In this paper, we discuss improved methods that
utilize Bayesian inference to obtain accurate estimates and precise credibility
intervals. The inferential methods are derived for both continuous and discrete
distributions. These methods reveal that objective Bayesian approaches return
nearly unbiased estimates for the parameters of both models. Notably, in the
continuous case, we identify an explicit posterior distribution. This work
enhances the power of goodness-of-fit tests, enabling us to accurately discern
whether a network or any other dataset adheres to a power-law distribution. We
apply the proposed approach to fit degree distributions for more than 5,000
synthetic networks and over 3,000 real networks. The results indicate that our
method is more suitable in practice, as it yields a frequency of acceptance
close to the specified nominal level.
