updated special pages

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

Author: JoramSoch

S/Model_Selection.md

@@ -4,7 +4,7 @@ title: "Special: Model Selection Criteria"
 ---
 
 
-**Proofs** and *Definitions* on [Model Selection Criteria](/I/Table_of_Contents#Model%20Selection) in the StatProofBook, as of 2020-09-09.
+**Proofs** and *Definitions* on [Model Selection Criteria](/I/Table_of_Contents#Model%20Selection) in the StatProofBook, as of 2020-12-02.
 
 | Criterion | Definition | Derivation | Relationships | Other |
 |:--------- |:---------- |:---------- |:------------- |:----- |
@@ -19,7 +19,7 @@ title: "Special: Model Selection Criteria"
 | **Bayesian<br>model selection** |  |  |  |  |
 | Log model evidence | *[lme](/D/lme)* | **[lme-der](/P/lme-der)** |  | **[lme-anc](/P/lme-anc)** |
 | Log family evidence | *[lfe](/D/lfe)* | **[lfe-der](/P/lfe-der)** | **[lfe-lme](/P/lfe-lme)** |  |
-| Bayes factor | *[bf](/D/bf)* |  |  | **[bf-trans](/P/bf-trans)**<br>**[bf-sddr](/P/bf-sddr)**<br>**[bf-ep](/P/bf-ep)** |
 | Log Bayes factor | *[lbf](/D/lbf)* | **[lbf-der](/P/lbf-der)** | **[lbf-lme](/P/lbf-lme)** |  |
+| Bayes factor | *[bf](/D/bf)* |  |  | **[bf-trans](/P/bf-trans)**<br>**[bf-sddr](/P/bf-sddr)**<br>**[bf-ep](/P/bf-ep)** |
 | Posterior model probability | *[pmp](/D/pmp)* | **[pmp-der](/P/pmp-der)** | **[pmp-bf](/P/pmp-bf)**<br>**[pmp-lbf](/P/pmp-lbf)**<br>**[pmp-lme](/P/pmp-lme)** |  |
 | Bayesian model averaging | *[bma](/D/bma)* | **[bma-der](/P/bma-der)** | **[bma-lme](/P/bma-lme)** |  |

S/Probability_Distributions.md

@@ -4,29 +4,30 @@ title: "Special: Probability Distributions"
 ---
 
 
-**Proofs** and *Definitions* on [Probability Distributions](/I/Table_of_Contents#Probability%20Distributions) in the StatProofBook, as of 2020-10-08.
+**Proofs** and *Definitions* on [Probability Distributions](/I/Table_of_Contents#Probability%20Distributions) in the StatProofBook, as of 2020-12-02.
 
-| Distribution | Def | PDF | CDF | QF | Mean | Med | Mode | Var | Ent | KL | Marg | Cond | Other |
-|:------------ |:--- |:--- |:--- |:-- |:---- |:--- |:---- |:--- |:--- |:-- |:---- |:---- |:----- |
-| **Univariate<br>discrete<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |
-| Discrete uniform distribution | *[duni](/D/duni)* | **[duni-pmf](/P/duni-pmf)** | **[duni-cdf](/P/duni-cdf)** | **[duni-qf](/P/duni-qf)** |  |  |  |  |  |  |  |  |  |
-| Bernoulli distribution | *[bern](/D/bern)* | **[bern-pmf](/P/bern-pmf)** |  |  | **[bern-mean](/P/bern-mean)** |  |  |  |  |  |  |  |  |
-| Binomial distribution | *[bin](/D/bin)* | **[bin-pmf](/P/bin-pmf)** |  |  | **[bin-mean](/P/bin-mean)** |  |  |  |  |  |  |  |  |
-| Poisson distribution | *[poiss](/D/poiss)* | **[poiss-pmf](/P/poiss-pmf)** |  |  | **[poiss-mean](/P/poiss-mean)** |  |  |  |  |  |  |  |  |
-| **Multivariate<br>discrete<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |
-| Categorical distribution | *[cat](/D/cat)* | **[cat-pmf](/P/cat-pmf)** |  |  | **[cat-mean](/P/cat-mean)** |  |  |  |  |  |  |  |  |
-| Multinomial distribution | *[mult](/D/mult)* | **[mult-pmf](/P/mult-pmf)** |  |  | **[mult-mean](/P/mult-mean)** |  |  |  |  |  |  |  |  |
-| **Univariate<br>continuous<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |
-| Continuous uniform distribution | *[cuni](/D/cuni)* | **[cuni-pdf](/P/cuni-pdf)** | **[cuni-cdf](/P/cuni-cdf)** | **[cuni-qf](/P/cuni-qf)** | **[cuni-mean](/P/cuni-mean)** | **[cuni-med](/P/cuni-med)** | **[cuni-mode](/P/cuni-mode)** |  |  |  |  |  |  |
-| Normal distribution | *[norm](/D/norm)*<br>*[snorm](/D/snorm)* | **[norm-pdf](/P/norm-pdf)** | **[norm-cdf](/P/norm-cdf)**<br>**[norm-cdfwerf](/P/norm-cdfwerf)** | **[norm-qf](/P/norm-qf)** | **[norm-mean](/P/norm-mean)** | **[norm-med](/P/norm-med)** | **[norm-mode](/P/norm-mode)** | **[norm-var](/P/norm-var)** | **[norm-dent](/P/norm-dent)** |  |  |  | **[norm-snorm](/P/norm-snorm)**<br>**[norm-mgf](/P/norm-mgf)**<br>**[norm-fwhm](/P/norm-fwhm)** |
-| Gamma distribution | *[gam](/D/gam)*<br>*[sgam](/D/sgam)* | **[gam-pdf](/P/gam-pdf)** |  |  | **[gam-mean](/P/gam-mean)**<br>**[gam-logmean](/P/gam-logmean)** |  |  | **[gam-var](/P/gam-var)** |  | **[gam-kl](/P/gam-kl)** |  |  | **[gam-sgam](/P/gam-sgam)** |
-| Exponential distribution | *[exp](/D/exp)* | **[exp-pdf](/P/exp-pdf)** | **[exp-cdf](/P/exp-cdf)** | **[exp-qf](/P/exp-qf)** | **[exp-mean](/P/exp-mean)** | **[exp-med](/P/exp-med)** | **[exp-mode](/P/exp-mode)** |  |  |  |  |  | **[exp-gam](/P/exp-gam)** |
-| Beta distribution | *[beta](/D/beta)* | **[beta-pdf](/P/beta-pdf)** |  |  |  |  |  |  |  |  |  |  |  |
-| Wald distribution | *[wald](/D/wald)* | **[wald-pdf](/P/wald-pdf)** |  |  | **[wald-mean](/P/wald-mean)** |  |  | **[wald-var](/P/wald-var)** |  |  |  |  | **[wald-mgf](/P/wald-mgf)** |
-| **Multivariate<br>continuous<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |
-| Multivariate normal distribution | *[mvn](/D/mvn)* | **[mvn-pdf](/P/mvn-pdf)** |  |  |  |  |  |  | **[mvn-dent](/P/mvn-dent)** | **[mvn-kl](/P/mvn-kl)** | **[mvn-marg](/P/mvn-marg)** | **[mvn-cond](/P/mvn-cond)** | **[mvn-ltt](/P/mvn-ltt)** |
-| Normal-gamma distribution | *[ng](/D/ng)* | **[ng-pdf](/P/ng-pdf)** |  |  |  |  |  |  |  | **[ng-kl](/P/ng-kl)** | **[ng-marg](/P/ng-marg)** | **[ng-cond](/P/ng-cond)** |  |
-| Dirichlet distribution | *[dir](/D/dir)* | **[dir-pdf](/P/dir-pdf)** |  |  |  |  |  |  |  |  |  |  |  |
-| **Matrix-variate<br>continuous<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |
-| Matrix-normal distribution | *[matn](/D/matn)* | **[matn-pdf](/P/matn-pdf)** |  |  |  |  |  |  |  |  |  |  | **[matn-mvn](/P/matn-mvn)**<br>**[matn-ltt](/P/matn-ltt)**<br>**[matn-trans](/P/matn-trans)** |
-| Wishart distribution | *[wish](/D/wish)* |  |  |  |  |  |  |  |  |  |  |  |  |
+| Distribution | Def | PDF | CDF | QF | MGF | Mean | Med | Mode | Var | Ent | KL | Marg | Cond | Other |
+|:------------ |:--- |:--- |:--- |:-- |:--- |:---- |:--- |:---- |:--- |:--- |:-- |:---- |:---- |:----- |
+| **Univariate<br>discrete<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
+| Discrete uniform distribution | *[duni](/D/duni)* | **[duni-pmf](/P/duni-pmf)** | **[duni-cdf](/P/duni-cdf)** | **[duni-qf](/P/duni-qf)** |  |  |  |  |  |  |  |  |  |  |
+| Bernoulli distribution | *[bern](/D/bern)* | **[bern-pmf](/P/bern-pmf)** |  |  |  | **[bern-mean](/P/bern-mean)** |  |  |  |  |  |  |  |  |
+| Binomial distribution | *[bin](/D/bin)* | **[bin-pmf](/P/bin-pmf)** |  |  |  | **[bin-mean](/P/bin-mean)** |  |  |  |  |  |  |  |  |
+| Poisson distribution | *[poiss](/D/poiss)* | **[poiss-pmf](/P/poiss-pmf)** |  |  |  | **[poiss-mean](/P/poiss-mean)** |  |  |  |  |  |  |  |  |
+| **Multivariate<br>discrete<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
+| Categorical distribution | *[cat](/D/cat)* | **[cat-pmf](/P/cat-pmf)** |  |  |  | **[cat-mean](/P/cat-mean)** |  |  |  |  |  |  |  |  |
+| Multinomial distribution | *[mult](/D/mult)* | **[mult-pmf](/P/mult-pmf)** |  |  |  | **[mult-mean](/P/mult-mean)** |  |  |  |  |  |  |  |  |
+| **Univariate<br>continuous<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
+| Continuous uniform distribution | *[cuni](/D/cuni)* | **[cuni-pdf](/P/cuni-pdf)** | **[cuni-cdf](/P/cuni-cdf)** | **[cuni-qf](/P/cuni-qf)** |  | **[cuni-mean](/P/cuni-mean)** | **[cuni-med](/P/cuni-med)** | **[cuni-mode](/P/cuni-mode)** |  |  |  |  |  |  |
+| Normal distribution | *[norm](/D/norm)*<br>*[snorm](/D/snorm)* | **[norm-pdf](/P/norm-pdf)** | **[norm-cdf](/P/norm-cdf)**<br>**[norm-cdfwerf](/P/norm-cdfwerf)** | **[norm-qf](/P/norm-qf)** | **[norm-mgf](/P/norm-mgf)** | **[norm-mean](/P/norm-mean)** | **[norm-med](/P/norm-med)** | **[norm-mode](/P/norm-mode)** | **[norm-var](/P/norm-var)** | **[norm-dent](/P/norm-dent)** | **[norm-kl](/P/norm-kl)** |  |  | **[norm-snorm](/P/norm-snorm)**<br>**[norm-gi](/P/norm-gi)**<br>**[norm-fwhm](/P/norm-fwhm)** |
+| Gamma distribution | *[gam](/D/gam)*<br>*[sgam](/D/sgam)* | **[gam-pdf](/P/gam-pdf)** | **[gam-cdf](/P/gam-cdf)** | **[gam-qf](/P/gam-qf)** |  | **[gam-mean](/P/gam-mean)**<br>**[gam-logmean](/P/gam-logmean)**<br>**[gam-xlogx](/P/gam-xlogx)** |  |  | **[gam-var](/P/gam-var)** |  | **[gam-kl](/P/gam-kl)** |  |  | **[gam-sgam](/P/gam-sgam)** |
+| Exponential distribution | *[exp](/D/exp)* | **[exp-pdf](/P/exp-pdf)** | **[exp-cdf](/P/exp-cdf)** | **[exp-qf](/P/exp-qf)** |  | **[exp-mean](/P/exp-mean)** | **[exp-med](/P/exp-med)** | **[exp-mode](/P/exp-mode)** |  |  |  |  |  | **[exp-gam](/P/exp-gam)** |
+| Chi-square distribution | *[chi2](/D/chi2)* | **[chi2-pdf](/P/chi2-pdf)** |  |  |  |  |  |  |  |  |  |  |  | **[chi2-gam](/P/chi2-gam)**<br>**[chi2-mom](/P/chi2-mom)** |
+| Beta distribution | *[beta](/D/beta)* | **[beta-pdf](/P/beta-pdf)** | **[beta-cdf](/P/beta-cdf)** |  | **[beta-mgf](/P/beta-mgf)** |  |  |  |  |  |  |  |  |  |
+| Wald distribution | *[wald](/D/wald)* | **[wald-pdf](/P/wald-pdf)** |  |  | **[wald-mgf](/P/wald-mgf)** | **[wald-mean](/P/wald-mean)** |  |  | **[wald-var](/P/wald-var)** |  |  |  |  |  |
+| **Multivariate<br>continuous<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
+| Multivariate normal distribution | *[mvn](/D/mvn)* | **[mvn-pdf](/P/mvn-pdf)** |  |  |  |  |  |  |  | **[mvn-dent](/P/mvn-dent)** | **[mvn-kl](/P/mvn-kl)** | **[mvn-marg](/P/mvn-marg)** | **[mvn-cond](/P/mvn-cond)** | **[mvn-ltt](/P/mvn-ltt)** |
+| Normal-gamma distribution | *[ng](/D/ng)* | **[ng-pdf](/P/ng-pdf)** |  |  |  |  |  |  |  |  | **[ng-kl](/P/ng-kl)** | **[ng-marg](/P/ng-marg)** | **[ng-cond](/P/ng-cond)** |  |
+| Dirichlet distribution | *[dir](/D/dir)* | **[dir-pdf](/P/dir-pdf)** |  |  |  |  |  |  |  |  |  |  |  | **[dir-ep](/P/dir-ep)** |
+| **Matrix-variate<br>continuous<br>distributions** |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
+| Matrix-normal distribution | *[matn](/D/matn)* | **[matn-pdf](/P/matn-pdf)** |  |  |  |  |  |  |  |  |  |  |  | **[matn-mvn](/P/matn-mvn)**<br>**[matn-ltt](/P/matn-ltt)**<br>**[matn-trans](/P/matn-trans)** |
+| Wishart distribution | *[wish](/D/wish)* |  |  |  |  |  |  |  |  |  |  |  |  |  |

S/Statistical_Models.md

@@ -4,10 +4,10 @@ title: "Special: Statistical Models"
 ---
 
 
-**Proofs** and *Definitions* on [Statistical Models](/I/Table_of_Contents#Statistical%20Models) in the StatProofBook, as of 2020-09-09.
+**Proofs** and *Definitions* on [Statistical Models](/I/Table_of_Contents#Statistical%20Models) in the StatProofBook, as of 2020-12-02.
 
 | Model | Definition | Estimation | Maximum<br>likelihood<br>estimation | Conjugate<br>prior | Posterior<br>distribution | Log<br>model<br>evidence | Other |
-|:----- |:---------- |:---------- |:----------------------------------- |:------------------------------- |:------------------------- |:--------------------- |:----- |
+|:----- |:---------- |:---------- |:----------------------------------- |:------------------ |:------------------------- |:------------------------ |:----- |
 | **Univariate<br>normal data** |  |  |  |  |  |  |  |
 | Multiple linear regression | *[mlr](/D/mlr)* | **[mlr-ols](/P/mlr-ols)**<br>**[mlr-wls](/P/mlr-wls)** | **[mlr-mle](/P/mlr-mle)** |  |  |  | **[mlr-pss](/P/mlr-pss)**<br>**[mlr-mat](/P/mlr-mat)**<br>**[mlr-idem](/P/mlr-idem)** |
 | Bayesian linear regression |  |  |  | **[blr-prior](/P/blr-prior)** | **[blr-post](/P/blr-post)** | **[blr-lme](/P/blr-lme)** | **[blr-pp](/P/blr-pp)**<br>**[blr-pcr](/P/blr-pcr)** |
@@ -19,7 +19,8 @@ title: "Special: Statistical Models"
 | Poisson distribution with exposure values | *[poissexp](/D/poissexp)* |  |  | **[poissexp-prior](/P/poissexp-prior)** | **[poissexp-post](/P/poissexp-post)** | **[poissexp-lme](/P/poissexp-lme)** |  |
 | **Probability data** |  |  |  |  |  |  |  |
 | Beta-distributed data | *[beta](/D/beta-data)* | **[beta-mom](/P/beta-mom)** |  |  |  |  |  |
-| Logistic regression | *[logreg](/D/logreg)* |  |  |  |  |  | **[logreg-pnlo](/P/logreg-pnlo)**<br>**[logreg-lonp](/P/logreg-lonp)** |
+| Dirichlet-distributed data | *[dir](/D/dir-data)* |  | **[dir-mle](/P/dir-mle)** |  |  |  |  |
 | **Categorical data** |  |  |  |  |  |  |  |
 | Binomial observations | *[bin](/D/bin-data)* |  |  | **[bin-prior](/P/bin-prior)** | **[bin-post](/P/bin-post)** | **[bin-lme](/P/bin-lme)** |  |
-| Multinomial observations | *[mult](/D/mult-data)* |  |  | **[mult-prior](/P/mult-prior)** | **[mult-post](/P/mult-post)** | **[mult-lme](/P/mult-lme)** |  |
+| Multinomial observations | *[mult](/D/mult-data)* |  |  | **[mult-prior](/P/mult-prior)** | **[mult-post](/P/mult-post)** | **[mult-lme](/P/mult-lme)** |  |
+| Logistic regression | *[logreg](/D/logreg)* |  |  |  |  |  | **[logreg-pnlo](/P/logreg-pnlo)**<br>**[logreg-lonp](/P/logreg-lonp)** |