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)	PSI]] between distributions and is given as

The JSD 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