Does anyone know a list of analytics solutions to KL divergences of commonly used distributions.

For example, 2 Normally Distributed Random Variables have a nicely formulated analytic solution.

Approximations should be fine too, I just need this for some optimization play where i don't have the computational resource to solve it through MC methods

  • 2
    $\begingroup$ If your distributions are both in the exponential family of distributions, then there is a general expression that can be derived - see this paper: web.archive.org/web/20190331194854/https://… $\endgroup$ Jul 4, 2019 at 22:05
  • $\begingroup$ @Don This was wonderful! thank you! $\endgroup$
    – mshlis
    Jul 5, 2019 at 11:45

1 Answer 1


First, much information can be found by searching this site. For exponential families see this paper (given in a comment above.) For skew distributions some information is here. For Pareto distributions here. Weibull distributions. Generalized gamma distributions.

$=$1&isAllowed$=$y" rel="nofollow noreferrer">A somewhat related useful paper.


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