# What tests can I use to compare these two probability distributions

I am trying to compare two one-dimensional distributions. I am using Kullback-Leibler divergence function for this but it requires me to have both the distributions of equal length. I am not sure how I can make the distributions of equal length without disturbing the original distributions(i.e. if I add zeroes to the distribution smaller in size, the probability of value 0 in that distribution will become very high.)

The probability densities of both my distributions are as shown in the below figure,

Note that, the N=235 refers to the bigger distribution size and doesn't imply that both distributions are of size 235.

Please suggest some way that I can use Kullback-Leibler divergence for this problem. Some input on other methods/tests which can be used for comparison will be appreciated as well.

• Your description is a bit confusing. A distribution doesn't have an $n$. Are you using the word distribution to refer to a sample, or to the length of a sequence of values where the density has been estimated, or something else? – Glen_b Mar 26 '16 at 0:59
• @Glen_b yes my N represents length of sequence of values where the density has been estimated. – Kunal Parmar Mar 26 '16 at 21:35