  The use of objective prior in Bayesian applications has become a common
practice to analyze data without subjective information. Formal rules usually
obtain these priors distributions, and the data provide the dominant
information in the posterior distribution. However, these priors are typically
improper and may lead to improper posterior. Here, we show, for a general
family of distributions, that the obtained objective priors for the parameters
either follow a power-law distribution or has an asymptotic power-law behavior.
As a result, we observed that the exponents of the model are between 0.5 and 1.
Understand these behaviors allow us to easily verify if such priors lead to
proper or improper posteriors directly from the exponent of the power-law. The
general family considered in our study includes essential models such as
Exponential, Gamma, Weibull, Nakagami-m, Haf-Normal, Rayleigh, Erlang, and
Maxwell Boltzmann distributions, to list a few. In summary, we show that
comprehending the mechanisms describing the shapes of the priors provides
essential information that can be used in situations where additional
complexity is presented.
