  Given an arbitrary continuous probability density function, it is introduced
a conjugated probability density, which is defined through the Shannon
information associated with its cumulative distribution function. These new
densities are computed from a number of standard distributions, including
uniform, normal, exponential, Pareto, logistic, Kumaraswamy, Rayleigh, Cauchy,
Weibull, and Maxwell-Boltzmann. The case of joint information-weighted
probability distribution is assessed. An additive property is derived in the
case of independent variables. One-sided and two-sided information-weighting
are considered. The asymptotic behavior of the tail of the new distributions is
examined. It is proved that all probability densities proposed here define
heavy-tailed distributions. It is shown that the weighting of distributions
regularly varying with extreme-value index $\alpha > 0$ still results in a
regular variation distribution with the same index. This approach can be
particularly valuable in applications where the tails of the distribution play
a major role.
