  We consider the detection of multiple outliers in Exponential and Pareto
samples -- as well as general samples that have approximately Exponential or
Pareto tails, thanks to Extreme Value Theory. It is shown that a simple
"robust" modification of common test statistics makes inward sequential testing
-- formerly relegated within the literature since the introduction of outward
testing -- as powerful as, and potentially less error prone than, outward
tests. Moreover, inward testing does not require the complicated type 1 error
control of outward tests. A variety of test statistics, employed in both block
and sequential tests, are compared for their power and errors, in cases
including no outliers, dispersed outliers (the classical slippage alternative),
and clustered outliers (a case seldom considered). We advocate a density
mixture approach for detecting clustered outliers. Tests are found to be highly
sensitive to the correct specification of the main distribution
(Exponential/Pareto), exposing high potential for errors in inference. Further,
in five case studies -- financial crashes, nuclear power generation accidents,
stock market returns, epidemic fatalities, and cities within countries --
significant outliers are detected and related to the concept of "Dragon King"
events, defined as meaningful outliers of unique origin.
