Merge pull request #90 from StatProofBook/master

update to master

Author: JoramSoch

I/PbA.md

@@ -8,7 +8,7 @@ title: "Proof by Author"
 
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 
-### JoramSoch (313 proofs)
+### JoramSoch (315 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -186,6 +186,7 @@ title: "Proof by Author"
 - [Non-negativity of the Shannon entropy](/P/ent-nonneg)
 - [Non-negativity of the variance](/P/var-nonneg)
 - [Non-symmetry of the Kullback-Leibler divergence](/P/kl-nonsymm)
+- [Normal distribution is a special case of multivariate normal distribution](/P/norm-mvn)
 - [Normal distribution maximizes differential entropy for fixed variance](/P/norm-maxent)
 - [Normal-gamma distribution is a special case of normal-Wishart distribution](/P/ng-nw)
 - [One-sample t-test for independent observations](/P/ug-ttest1)
@@ -299,6 +300,7 @@ title: "Proof by Author"
 - [Second central moment is variance](/P/momcent-2nd)
 - [Simple linear regression is a special case of multiple linear regression](/P/slr-mlr)
 - [Sums of squares for simple linear regression](/P/slr-sss)
+- [t-distribution is a special case of multivariate t-distribution](/P/t-mvt)
 - [The p-value follows a uniform distribution under the null hypothesis](/P/pval-h0)
 - [The regression line goes through the center of mass point](/P/slr-comp)
 - [The residuals and the covariate are uncorrelated in simple linear regression](/P/slr-rescorr)

I/PbN.md

@@ -336,3 +336,5 @@ title: "Proof by Number"
 | P328 | gam-wish | [Gamma distribution is a special case of Wishart distribution](/P/gam-wish) | JoramSoch | 2022-07-14 |
 | P329 | mlr-glm | [Multiple linear regression is a special case of the general linear model](/P/mlr-glm) | JoramSoch | 2022-07-21 |
 | P330 | mvn-matn | [Multivariate normal distribution is a special case of matrix-normal distribution](/P/mvn-matn) | JoramSoch | 2022-07-31 |
+| P331 | norm-mvn | [Normal distribution is a special case of multivariate normal distribution](/P/norm-mvn) | JoramSoch | 2022-08-19 |
+| P332 | t-mvt | [t-distribution is a special case of multivariate t-distribution](/P/t-mvt) | JoramSoch | 2022-08-25 |

I/PbT.md

@@ -228,6 +228,7 @@ title: "Proof by Topic"
 - [Non-negativity of the Shannon entropy](/P/ent-nonneg)
 - [Non-negativity of the variance](/P/var-nonneg)
 - [Non-symmetry of the Kullback-Leibler divergence](/P/kl-nonsymm)
+- [Normal distribution is a special case of multivariate normal distribution](/P/norm-mvn)
 - [Normal distribution maximizes differential entropy for fixed variance](/P/norm-maxent)
 - [Normal-gamma distribution is a special case of normal-Wishart distribution](/P/ng-nw)
 
@@ -364,6 +365,7 @@ title: "Proof by Topic"
 
 ### T
 
+- [t-distribution is a special case of multivariate t-distribution](/P/t-mvt)
 - [The p-value follows a uniform distribution under the null hypothesis](/P/pval-h0)
 - [The regression line goes through the center of mass point](/P/slr-comp)
 - [The residuals and the covariate are uncorrelated in simple linear regression](/P/slr-rescorr)

I/PwS.md

@@ -65,7 +65,6 @@ title: "Proofs without Source"
 - [Mode of the continuous uniform distribution](/P/cuni-med)
 - [Mode of the exponential distribution](/P/exp-mode)
 - [Mode of the normal distribution](/P/norm-mode)
-- [Multivariate normal distribution is a special case of matrix-normal distribution](/P/mvn-matn)
 - [Necessary and sufficient condition for independence of multivariate normal random variables](/P/mvn-ind)
 - [Normal-gamma distribution is a special case of normal-Wishart distribution](/P/ng-nw)
 - [Ordinary least squares for simple linear regression](/P/slr-ols2)

P/mvn-matn.md

@@ -19,7 +19,7 @@ sources:
     title: "Matrix normal distribution"
     in: "Wikipedia, the free encyclopedia"
     pages: "retrieved on 2022-07-31"
-    url: "https://en.wikipedia.org/wiki/Matrix_normal_distribution"
+    url: "https://en.wikipedia.org/wiki/Matrix_normal_distribution#Definition"
 
 proof_id: "P330"
 shortcut: "mvn-matn"
@@ -38,7 +38,7 @@ $$
 
 Setting $p = 1$, $X = x$, $M = \mu$, $U = \Sigma$ and $V = 1$, we obtain
 
-$$ \label{eq:exp-pdf}
+$$ \label{eq:mvn-pdf}
 \begin{split}
 \mathcal{MN}(x; \mu, \Sigma, 1) &= \frac{1}{\sqrt{(2\pi)^{n} |1|^n |\Sigma|^1}} \cdot \exp\left[-\frac{1}{2} \mathrm{tr}\left( 1^{-1} (x-\mu)^\mathrm{T} \, \Sigma^{-1} (x-\mu) \right) \right] \\
 &= \frac{1}{\sqrt{(2\pi)^{n} |\Sigma|}} \cdot \exp\left[-\frac{1}{2} (x-\mu)^\mathrm{T} \, \Sigma^{-1} (x-\mu) \right]

P/norm-mvn.md

@@ -11,7 +11,7 @@ title: "Normal distribution is a special case of multivariate normal distributio
 chapter: "Probability Distributions"
 section: "Univariate continuous distributions"
 topic: "Normal distribution"
-theorem: "Special case of matrix-normal distribution"
+theorem: "Special case of multivariate normal distribution"
 
 sources:
   - authors: "Wikipedia"
@@ -22,7 +22,7 @@ sources:
     url: "https://en.wikipedia.org/wiki/Multivariate_normal_distribution"
 
 proof_id: "P331"
-shortcut: "norm-snorm"
+shortcut: "norm-mvn"
 username: "JoramSoch"
 ---