For the requested examples see <A HREF="http://arxiv.org/abs/1206.2459">Rényi Divergence and Kullback-Leibler Divergence</A> (2012).

• *Two continuous distributions:* Equation 10 gives the Rényi divergence between two Gaussian distributions (mean $\mu_i$, variance $\sigma_i$):

$$
  D_\alpha\Big({\cal N}(\mu_0,\sigma_0^2)\|{\cal N}(\mu_1,\sigma_1^2)\Big)
    = \frac{\alpha(\mu_1 - \mu_0)^2}{2\sigma_\alpha^2}
      + \frac{1}{1-\alpha} \log\left(
      \frac{\sigma_\alpha}{\sigma_0^{1-\alpha}\sigma_1^\alpha}\right),
$$
for $\sigma_\alpha^2 = (1-\alpha)\sigma_0^2 + \alpha
\sigma_1^2 > 0$

• *Two discrete distributions:* Figures 2 and 3 show the Rényi divergence $D_\alpha(P||Q)$ for fixed $Q$ as $P$ varies over a sample space containing two or three elements.


<IMG SRC="https://ilorentz.org/beenakker/MO/Renyi.png" WIDTH="400" />