for example, in a discrete distribution A
P(X) = 0.999 when x = 0 P(X) = 0.001 when x = 1000 E(X) = 1 Var(X) = 1000-1=999
compared to B
P(X) = 0.6 when x = 0 P(X) = 0.2 when x = 1 P(X) = 0.2/2 when x = 2 P(X) = 0.2/4 when x = 4 P(X) = 0.2/4 when x = 8 E(X) = 1 =A Var(X) = 0.2+0.4+0.8+3.2-1=3.6 <<A
However B seems more volatile(instable) than A. What is the common correct stats to measure this sort of thing?
Entropy might be a good candidate, however it doesn't look into the information itself (it only cares about the chance). I feel the time series graph of a fair coin which could score (0 or 1) is less volatile / more stable than a fair coin which could score (0 or 100).