  A confidence distribution is a distribution for a parameter of interest based
on a parametric statistical model. As such, it serves the same purpose for
frequentist statisticians as a posterior distribution for Bayesians, since it
allows to reach point estimates, to assess their precision, to set up tests
along with measures of evidence, to derive confidence intervals, comparing the
parameter of interest with other parameters from other studies, etc. A general
recipe for deriving confidence distributions is based on classical pivotal
quantities and their exact or approximate distributions.
  However, in the presence of model misspecifications or outlying values in the
observed data, classical pivotal quantities, and thus confidence distributions,
may be inaccurate. The aim of this paper is to discuss the derivation and
application of robust confidence distributions. In particular, we discuss a
general approach based on the Tsallis scoring rule in order to compute a robust
confidence distribution. Examples and simulation results are discussed for some
problems often encountered in practice, such as the two-sample heteroschedastic
comparison, the receiver operating characteristic curves and regression models.
