# KL divergence between two univariate Poisson distributions

I found this awesome thread which shows KL divergence between two univariate Gaussians. I was wondering if the same formula worked for KL divergence b/w 2 univariate Poisson distributions.

Or should I use the general KL divergence formula and plug into it the pdf for a Poisson process: $$\int { pdf1(x)*{ log(pdf1(x)/pdf2(x))} }$$

where for Poisson is $$pdf(x) = (\lambda^x / x!)*e^{-\lambda}$$

$$\log\left (\frac {f_1}{f_2}\right)=x\log\left (\frac {\lambda_1}{\lambda_2}\right)+\lambda_2-\lambda_1$$
Then you take expectation of this expression wrt $f_1$, which simply replaces $x$ with its expectation (in this case). So you have:
$$D_{KL} (f_1||f_2)=\lambda_1\log\left (\frac {\lambda_1}{\lambda_2}\right)+\lambda_2-\lambda_1$$