Response of JSD and PSI to a rare event

Consider two discrete probability distributions, and .

Event
A	0.50	0.50
B	0.30	0.30
C	0.15	0.15
D	0.04	0.045
E	0.01	0.005
The [[Population stability index, (Jeffreys distance, PSI)	population stability index]] between distributions and is given as

The Jensen-Shannon divergence is given as

We can calculate the contribution of each outcome to these two formulae through direct computation.

Event	PSI Contribution	JSD Contribution
A	0	0
B	0	0
C	0	0
D	0.0002385	0.000763
E	0.0034655	0.00042475
Total	0.003704	0.00118775