Population stability index - division by zero Population stability index quantifies the change of a distribution of a variable by comparing data samples in two time periods. It is very commonly used to measure shifts in scores.
It is calculated as follows:
1) The sample from base period is discretized. Usually it is partitioned into deciles
2) The sample from target period is discretized using the same intervals as in first step
$PSI = \sum_{i} (A_{i} - B_{i}) \cdot ln(\frac{A_{i}}{B_{i}})$
Where:
$A_{i}$ - share of i-th bin in base period.
$B_{i}$ - share of i-th bin in target period.
Question: What should be done when one of the bins from target sample is empty? 
 A: I guess you could consider the empty bins as filled with a very small number. This retains the information and avoids division by zero. And, of course, this way you keep the original bins, which is a good thing.
A: One way is to assign one count to such bins and then calculate the fraction considering this new point:
counts[counts==0] = 1
fract = counts/sum(counts)

If your sample is large enough that few counts are negligible, then I think it is a good approximation. The information that you have after adding these "phantom" counts is almost the same (always considering the validity of new points in your sample): very very very ... few points from your sample fall down in these bins.
A: Could you skip it?
That is, could you understand it as zero？
The division by zero is uniquely and reasonably determined as 1/0=0/0=z/0=0 in the natural extensions of fractions. We have to change our basic ideas for our space and world
Division by Zero z/0 = 0 in Euclidean Spaces
Hi roshi Michiwaki, Hiroshi Okumura and Saburou Saitoh
International Journal of Mathematics and Computation Vol. 28(2017); Issue  1, 2017), 1
-16. 　
http://www.scirp.org/journal/alamt 　 　 http://dx.doi.org/10.4236/alamt.2016.62007
http://www.ijapm.org/show-63-504-1.html
http://www.diogenes.bg/ijam/contents/2014-27-2/9/9.pdf
http://okmr.yamatoblog.net/division%20by%20zero/announcement%20326-%20the%20divi
http://okmr.yamatoblog.net/
Relations of 0 and infinity
Hiroshi Okumura, Saburou Saitoh　and Tsutomu Matsuura：
http://www.e-jikei.org/…/Camera%20ready%20manuscript_JTSS_A…
https://sites.google.com/site/sandrapinelas/icddea-2017
