In engineering/economic practices I encounter many applications that gaussian distribution is used to model the probability of events. I know that distributions like gaussian distribution have a definite variance and mean that gives us good information on the probability of events.
On the other hand mandelbrotian or fat-tailed distributions describe processes that outlier events are not as unlikely as processes that are modeled using gaussian/poisson/exponential distribution.
I see many processes that could be considered mandelbrotian but treated as gaussian (for example in economic predictions/forecast or some machine learning problems).
I wonder who gives us permission to use distributions like gaussian/poisson/exponential distribution with so much confidence in many applications?