A concentrated Cauchy distribution with finite moments

with two parameters, a (location) and b > 0 (scale), [2, p. 50]. The Cauchy distribution occurs in numerous applications, see, e.g., [3, p. 159]. A recent interest in C(a, b) is due to its “fat tails”, accounting for outliers (rare events) better than the more concentrated distributions commonly used, in particular the normal distribution. Indeed, these “rare” events with significant consequences (that may not be so rare, see, e.g., [4]), make the 6 σ paradigm useless in certain applications.