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The mode of the Pareto distribution is its lowest value.
To derive the mean of generalized Pareto distribution you must be good with numbers. You must be good in Calculus, Algebra and Statistics.
The total deviation from the mean for ANY distribution is always zero.
Divakar Sharma has written:
'On some estimators of the parameters of the Pareto distribution'
var(X) = (xm/a - 1)2 a/a-2 .
If a < or equal to 2, the variance does not exist.