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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, Probability density functions

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.

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    $\begingroup$ 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? $\endgroup$
    – Glen_b
    Commented Mar 26, 2016 at 0:59
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    $\begingroup$ @Glen_b yes my N represents length of sequence of values where the density has been estimated. $\endgroup$
    – Kunal Parmar
    Commented Mar 26, 2016 at 21:35

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Why do you want to use KL divergence for this problem? You basically have a 2-sample problem, and want to test if the distributions are equal. Depending on the specifics of your problem, which you did not tell us, there are many methods. And many posts on this site, some of them

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