I calculated the discrete probabilities for my project. I have two parameters k and l and I varied the third one which is the y axis (x values are log of the probabilities) in this enclosed picture.

The computation is quite expensive so I would like to figure out if I can approximate this by some known distributions. I have tried to fit beta negative binomial distribution
http://reference.wolfram.com/language/ref/BetaNegativeBinomialDistribution.html
for small value of k and l but it does not fit well. My function tends to peak at k.
Any suggestions on possible distributions that could fit this ?