updated index pages

The index pages were updated with the recently added proofs.

Author: JoramSoch

I/PbA.md

@@ -8,7 +8,7 @@ title: "Proof by Author"
 
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 
-### JoramSoch (392 proofs)
+### JoramSoch (393 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -140,6 +140,7 @@ title: "Proof by Author"
 - [Joint likelihood is the product of likelihood function and prior density](/P/jl-lfnprior)
 - [Kullback-Leibler divergence for the Bernoulli distribution](/P/bern-kl)
 - [Kullback-Leibler divergence for the binomial distribution](/P/bin-kl)
+- [Kullback-Leibler divergence for the continuous uniform distribution](/P/cuni-kl)
 - [Kullback-Leibler divergence for the Dirichlet distribution](/P/dir-kl)
 - [Kullback-Leibler divergence for the gamma distribution](/P/gam-kl)
 - [Kullback-Leibler divergence for the matrix-normal distribution](/P/matn-kl)

I/PbN.md

@@ -427,3 +427,4 @@ title: "Proof by Number"
 | P419 | bern-kl | [Kullback-Leibler divergence for the Bernoulli distribution](/P/bern-kl) | JoramSoch | 2023-10-13 |
 | P420 | bin-kl | [Kullback-Leibler divergence for the binomial distribution](/P/bin-kl) | JoramSoch | 2023-10-20 |
 | P421 | wald-skew | [Skewness of the Wald distribution](/P/wald-skew) | tomfaulkenberry | 2023-10-24 |
+| P422 | cuni-kl | [Kullback-Leibler divergence for the continuous uniform distribution](/P/cuni-kl) | JoramSoch | 2023-10-27 |

I/PbT.md

@@ -167,6 +167,7 @@ title: "Proof by Topic"
 
 - [Kullback-Leibler divergence for the Bernoulli distribution](/P/bern-kl)
 - [Kullback-Leibler divergence for the binomial distribution](/P/bin-kl)
+- [Kullback-Leibler divergence for the continuous uniform distribution](/P/cuni-kl)
 - [Kullback-Leibler divergence for the Dirichlet distribution](/P/dir-kl)
 - [Kullback-Leibler divergence for the gamma distribution](/P/gam-kl)
 - [Kullback-Leibler divergence for the matrix-normal distribution](/P/matn-kl)

I/PwS.md

@@ -46,6 +46,7 @@ title: "Proofs without Source"
 - [Gamma distribution is a special case of Wishart distribution](/P/gam-wish)
 - [Joint likelihood is the product of likelihood function and prior density](/P/jl-lfnprior)
 - [Kullback-Leibler divergence for the Bernoulli distribution](/P/bern-kl)
+- [Kullback-Leibler divergence for the continuous uniform distribution](/P/cuni-kl)
 - [Kullback-Leibler divergence for the matrix-normal distribution](/P/matn-kl)
 - [Kullback-Leibler divergence for the normal distribution](/P/norm-kl)
 - [Linear combination of independent normal random variables](/P/norm-lincomb)

P/cuni-kl.md

@@ -43,7 +43,7 @@ $$ \label{eq:KL-cont}
 \mathrm{KL}[P\,||\,Q] = \int_{\mathcal{X}} p(x) \, \ln \frac{p(x)}{q(x)} \, \mathrm{d}x \; .
 $$
 
-This means that the KL divergence of $P$ from $Q$ is only defined, if for all $x \in \mathcal{X}$, $q(x) = 0$ implies $p(x) = 0$. Thus, $\mathrm{KL}[P\,||\,Q]$ only exists, if $a_2 \leq a_1$ and $b_1 \leq b_2$, i.e. if $P$ only places non-zero probability where $Q$ also places non-zero probability, such that $q(x)$ is not zero for any $x \in \mathcal{X}$ where $p(x)$ is positive.
+This means that the KL divergence of $P$ from $Q$ is only defined, if for all $x \in \mathcal{X}$, $q(x) = 0$ implies $p(x) = 0$. Thus, $\mathrm{KL}[P\,\vert\vert\,Q]$ only exists, if $a_2 \leq a_1$ and $b_1 \leq b_2$, i.e. if $P$ only places non-zero probability where $Q$ also places non-zero probability, such that $q(x)$ is not zero for any $x \in \mathcal{X}$ where $p(x)$ is positive.
 
 If this requirement is fulfilled, we can write