  Estimating the location and scale parameters is common in statistics, using,
for instance, the well-known sample mean and standard deviation. However,
inference can be contaminated by the presence of outliers if modeling is done
with light-tailed distributions such as the normal distribution. In this paper,
we study robustness to outliers in location-scale parameter models using both
the Bayesian and frequentist approaches. We find sufficient conditions (e.g.,
on tail behavior of the model) to obtain whole robustness to outliers, in the
sense that the impact of the outliers gradually decreases to nothing as the
conflict grows infinitely. To this end, we introduce the family of
log-Pareto-tailed symmetric distributions that belongs to the larger family of
log-regularly varying distributions.
