updated index pages

The index pages were updated with the recently added proofs/definitions.

Author: JoramSoch

D/rvar-uni.md

@@ -29,7 +29,7 @@ username: "JoramSoch"
 
 **Definition:** Let $X$ be a [random variable](/D/rvar) with possible outcomes $\mathcal{X}$. Then,
 
-* $X$ is called a two-valued random variable or [random event](/D/reve), if $\mathcal{X}$ has two elements, e.g. $\mathcal{X} = \left\lbrace \mathrm{true}, \mathrm{false} \right\rbrace$ or $\mathcal{X} = \left\lbrace 1, 0 \right\rbrace$;
+* $X$ is called a two-valued random variable or [random event](/D/reve), if $\mathcal{X}$ has exactly two elements, e.g. $\mathcal{X} = \left\lbrace \mathrm{true}, \mathrm{false} \right\rbrace$ or $\mathcal{X} = \left\lbrace 1, 0 \right\rbrace$;
 
 * $X$ is called a univariate random variable or [random scalar](/D/rvar), if $\mathcal{X}$ is one-dimensional, i.e. (a subset of) the real numbers $\mathbb{R}$;
 

I/Definition_by_Author.md

@@ -4,7 +4,7 @@ title: "Definition by Author"
 ---
 
 
-### JoramSoch (108 definitions)
+### JoramSoch (111 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Bayesian information criterion](/D/bic)
@@ -38,6 +38,7 @@ title: "Definition by Author"
 - [Dirichlet-distributed data](/D/dir-data)
 - [Discrete and continuous random variable](/D/rvar-disc)
 - [Discrete uniform distribution](/D/duni)
+- [Empirical Bayesian log model evidence](/D/eblme)
 - [Estimation matrix](/D/emat)
 - [Exceedance probability](/D/prob-exc)
 - [Expected value](/D/mean)
@@ -111,8 +112,10 @@ title: "Definition by Author"
 - [Standardized moment](/D/mom-stand)
 - [Statistical independence](/D/ind)
 - [Total sum of squares](/D/tss)
+- [Uniform-prior log model evidence](/D/uplme)
 - [Univariate and multivariate random variable](/D/rvar-uni)
 - [Variance](/D/var)
+- [Variational Bayesian log model evidence](/D/vblme)
 - [Wishart distribution](/D/wish)
 
 ### StatProofBook (1 definition)

I/Definition_by_Number.md

@@ -119,3 +119,6 @@ title: "Definition by Number"
 | D110 | reve | [Random event](/D/reve) | JoramSoch | 2020-11-19 |
 | D111 | cvlme | [Cross-validated log model evidence](/D/cvlme) | JoramSoch | 2020-11-19 |
 | D112 | ind-cond | [Conditional independence](/D/ind-cond) | JoramSoch | 2020-11-19 |
+| D113 | uplme | [Uniform-prior log model evidence](/D/uplme) | JoramSoch | 2020-11-25 |
+| D114 | eblme | [Empirical Bayesian log model evidence](/D/eblme) | JoramSoch | 2020-11-25 |
+| D115 | vblme | [Variational Bayesian log model evidence](/D/vblme) | JoramSoch | 2020-11-25 |

I/Definition_by_Topic.md

@@ -53,6 +53,7 @@ title: "Definition by Topic"
 
 ### E
 
+- [Empirical Bayesian log model evidence](/D/eblme)
 - [Encompassing model](/D/encm)
 - [Estimation matrix](/D/emat)
 - [Exceedance probability](/D/prob-exc)
@@ -166,11 +167,13 @@ title: "Definition by Topic"
 
 ### U
 
+- [Uniform-prior log model evidence](/D/uplme)
 - [Univariate and multivariate random variable](/D/rvar-uni)
 
 ### V
 
 - [Variance](/D/var)
+- [Variational Bayesian log model evidence](/D/vblme)
 
 ### W
 

I/Proof_by_Author.md

@@ -4,7 +4,7 @@ title: "Proof by Author"
 ---
 
 
-### JoramSoch (186 proofs)
+### JoramSoch (189 proofs)
 
 - [(Non-)Multiplicativity of the expected value](/P/mean-mult)
 - [Additivity of the Kullback-Leibler divergence for independent distributions](/P/kl-add)
@@ -55,6 +55,7 @@ title: "Proof by Author"
 - [First central moment is zero](/P/momcent-1st)
 - [First raw moment is mean](/P/momraw-1st)
 - [Full width at half maximum for the normal distribution](/P/norm-fwhm)
+- [Gaussian integral](/P/norm-gi)
 - [Gibbs' inequality](/P/gibbs-ineq)
 - [Invariance of the Kullback-Leibler divergence under parameter transformation](/P/kl-inv)
 - [Invariance of the variance under addition of a constant](/P/var-inv)
@@ -104,6 +105,7 @@ title: "Proof by Author"
 - [Mode of the normal distribution](/P/norm-mode)
 - [Moment in terms of moment-generating function](/P/mom-mgf)
 - [Moment-generating function of linear combination of independent random variables](/P/mgf-lincomb)
+- [Moment-generating function of the beta distribution](/P/beta-mgf)
 - [Moment-generating function of the normal distribution](/P/norm-mgf)
 - [Monotonicity of the expected value](/P/mean-mono)
 - [Non-negativity of the Kullback-Leibler divergence](/P/kl-nonneg)
@@ -138,6 +140,7 @@ title: "Proof by Author"
 - [Probability density function of a strictly increasing function of a continuous random variable](/P/pdf-sifct)
 - [Probability density function of the Dirichlet distribution](/P/dir-pdf)
 - [Probability density function of the beta distribution](/P/beta-pdf)
+- [Probability density function of the chi-square distribution](/P/chi2-pdf)
 - [Probability density function of the continuous uniform distribution](/P/cuni-pdf)
 - [Probability density function of the exponential distribution](/P/exp-pdf)
 - [Probability density function of the gamma distribution](/P/gam-pdf)

I/Proof_by_Number.md

@@ -202,3 +202,6 @@ title: "Proof by Number"
 | P193 | norm-kl | [Kullback-Leibler divergence for the normal distribution](/P/norm-kl) | JoramSoch | 2020-11-19 |
 | P194 | gam-qf | [Quantile function of the gamma distribution](/P/gam-qf) | JoramSoch | 2020-11-19 |
 | P195 | beta-cdf | [Cumulative distribution function of the beta distribution](/P/beta-cdf) | JoramSoch | 2020-11-19 |
+| P196 | norm-gi | [Gaussian integral](/P/norm-gi) | JoramSoch | 2020-11-25 |
+| P197 | chi2-pdf | [Probability density function of the chi-square distribution](/P/chi2-pdf) | JoramSoch | 2020-11-25 |
+| P198 | beta-mgf | [Moment-generating function of the beta distribution](/P/beta-mgf) | JoramSoch | 2020-11-25 |

I/Proof_by_Topic.md

@@ -78,6 +78,7 @@ title: "Proof by Topic"
 
 ### G
 
+- [Gaussian integral](/P/norm-gi)
 - [Gibbs' inequality](/P/gibbs-ineq)
 
 ### I
@@ -144,6 +145,7 @@ title: "Proof by Topic"
 - [Moment in terms of moment-generating function](/P/mom-mgf)
 - [Moment-generating function of linear combination of independent random variables](/P/mgf-lincomb)
 - [Moment-generating function of the Wald distribution](/P/wald-mgf)
+- [Moment-generating function of the beta distribution](/P/beta-mgf)
 - [Moment-generating function of the normal distribution](/P/norm-mgf)
 - [Moments of the chi-square distribution](/P/chi2-mom)
 - [Monotonicity of the expected value](/P/mean-mono)
@@ -189,6 +191,7 @@ title: "Proof by Topic"
 - [Probability density function of the Dirichlet distribution](/P/dir-pdf)
 - [Probability density function of the Wald distribution](/P/wald-pdf)
 - [Probability density function of the beta distribution](/P/beta-pdf)
+- [Probability density function of the chi-square distribution](/P/chi2-pdf)
 - [Probability density function of the continuous uniform distribution](/P/cuni-pdf)
 - [Probability density function of the exponential distribution](/P/exp-pdf)
 - [Probability density function of the gamma distribution](/P/gam-pdf)