updated index pages

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

Author: JoramSoch

D/chi2.md

@@ -14,18 +14,18 @@ topic: "Chi-square distribution"
 definition: "Definition"
 
 sources:
- - authors: "Wikipedia"
-   year: 2020
-   title: "Chi-square distribution"
-   in: "Wikipedia, the free encyclopedia"
-   pages: "retrieved on 2020-10-12"
-   url: "https://en.wikipedia.org/wiki/Chi-square_distribution#Definitions"
- - authors: "Robert V. Hogg, Joseph W. McKean, Allen T. Craig"
-   year: 2018
-   title: "The χ2-Distribution"
-   in: "Introduction to Mathematical Statistics"
-   pages: "Pearson, Boston, 2019, p. 178, eq. 3.3.7"
-   url: "https://www.pearson.com/store/p/introduction-to-mathematical-statistics/P100000843744"
+  - authors: "Wikipedia"
+    year: 2020
+    title: "Chi-square distribution"
+    in: "Wikipedia, the free encyclopedia"
+    pages: "retrieved on 2020-10-12"
+    url: "https://en.wikipedia.org/wiki/Chi-square_distribution#Definitions"
+  - authors: "Robert V. Hogg, Joseph W. McKean, Allen T. Craig"
+    year: 2018
+    title: "The χ2-Distribution"
+    in: "Introduction to Mathematical Statistics"
+    pages: "Pearson, Boston, 2019, p. 178, eq. 3.3.7"
+    url: "https://www.pearson.com/store/p/introduction-to-mathematical-statistics/P100000843744"
 
 def_id: "D100"
 shortcut: "chi2"
@@ -37,7 +37,7 @@ username: "kjpetrykowski"
 
 $$ \label{eq:snorm}
 X_{i} \sim \mathcal{N}(0,1) \; .
-$$.
+$$
 
 Then, the sum of their squares follows a chi-square distribution with $k$ degrees of freedom:
 

I/Definition_by_Author.md

@@ -107,6 +107,10 @@ title: "Definition by Author"
 
 - [Definition Template](/D/-temp-)
 
+### kjpetrykowski (1 definition)
+
+- [Chi-square distribution](/D/chi2)
+
 ### tomfaulkenberry (3 definitions)
 
 - [Bayes factor](/D/bf)

I/Definition_by_Number.md

@@ -106,3 +106,4 @@ title: "Definition by Number"
 | D97 | mom-raw | [Raw moment](/D/mom-raw) | JoramSoch | 2020-10-08 |
 | D98 | mom-cent | [Central moment](/D/mom-cent) | JoramSoch | 2020-10-08 |
 | D99 | mom-stand | [Standardized moment](/D/mom-stand) | JoramSoch | 2020-10-08 |
+| D100 | chi2 | [Chi-square distribution](/D/chi2) | kjpetrykowski | 2020-10-13 |

I/Definition_by_Topic.md

@@ -23,6 +23,7 @@ title: "Definition by Topic"
 
 - [Categorical distribution](/D/cat)
 - [Central moment](/D/mom-cent)
+- [Chi-square distribution](/D/chi2)
 - [Coefficient of determination](/D/rsq)
 - [Conditional differential entropy](/D/dent-cond)
 - [Conditional entropy](/D/ent-cond)

I/Proof_by_Author.md

@@ -177,6 +177,11 @@ title: "Proof by Author"
 
 - [Proof Template](/P/-temp-)
 
+### kjpetrykowski (2 proofs)
+
+- [Chi-square distribution is a special case of gamma distribution](/P/chi2-gam)
+- [Moments of the chi-square distribution](/P/chi2-mom)
+
 ### tomfaulkenberry (7 proofs)
 
 - [Encompassing Prior Method for computing Bayes Factors](/P/bf-ep)

I/Proof_by_Number.md

@@ -180,3 +180,5 @@ title: "Proof by Number"
 | P171 | momraw-1st | [First raw moment is mean](/P/momraw-1st) | JoramSoch | 2020-10-08 |
 | P172 | momraw-2nd | [Relationship between second raw moment, variance and mean](/P/momraw-2nd) | JoramSoch | 2020-10-08 |
 | P173 | momcent-2nd | [Second central moment is variance](/P/momcent-2nd) | JoramSoch | 2020-10-08 |
+| P174 | chi2-gam | [Chi-square distribution is a special case of gamma distribution](/P/chi2-gam) | kjpetrykowski | 2020-10-12 |
+| P175 | chi2-mom | [Moments of the chi-square distribution](/P/chi2-mom) | kjpetrykowski | 2020-10-13 |

I/Proof_by_Topic.md

@@ -21,6 +21,7 @@ title: "Proof by Topic"
 
 ### C
 
+- [Chi-square distribution is a special case of gamma distribution](/P/chi2-gam)
 - [Concavity of the Shannon entropy](/P/ent-conc)
 - [Conditional distributions of the multivariate normal distribution](/P/mvn-cond)
 - [Conditional distributions of the normal-gamma distribution](/P/ng-cond)
@@ -134,6 +135,7 @@ title: "Proof by Topic"
 - [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 normal distribution](/P/norm-mgf)
+- [Moments of the chi-square distribution](/P/chi2-mom)
 - [Monotonicity of the expected value](/P/mean-mono)
 
 ### N

I/Proofs_without_Source.md

@@ -4,6 +4,7 @@ title: "Proofs without Source"
 ---
 
 
+- [Chi-square distribution is a special case of gamma distribution](/P/chi2-gam)
 - [Conditional distributions of the normal-gamma distribution](/P/ng-cond)
 - [Cumulative distribution function of the continuous uniform distribution](/P/cuni-cdf)
 - [Cumulative distribution function of the discrete uniform distribution](/P/duni-cdf)

I/Table_of_Contents.md

@@ -263,16 +263,21 @@ title: "Table of Contents"
    &emsp;&ensp; 3.4.7. **[Median](/P/exp-med)** <br>
    &emsp;&ensp; 3.4.8. **[Mode](/P/exp-mode)** <br>
 
-   3.5. Beta distribution <br>
-   &emsp;&ensp; 3.5.1. *[Definition](/D/beta)* <br>
-   &emsp;&ensp; 3.5.2. **[Probability density function](/P/beta-pdf)** <br>
-   
-   3.6. Wald distribution <br>
-   &emsp;&ensp; 3.6.1. *[Definition](/D/wald)* <br>
-   &emsp;&ensp; 3.6.2. **[Probability density function](/P/wald-pdf)** <br>
-   &emsp;&ensp; 3.6.3. **[Moment-generating function](/P/wald-mgf)** <br>
-   &emsp;&ensp; 3.6.4. **[Mean](/P/wald-mean)** <br>
-   &emsp;&ensp; 3.6.5. **[Variance](/P/wald-var)** <br>   
+   3.5. Chi-square distribution <br>
+   &emsp;&ensp; 3.5.1. *[Definition](/D/chi2)* <br>
+   &emsp;&ensp; 3.5.2. **[Special case of gamma distribution](/P/chi2-gam)** <br>
+   &emsp;&ensp; 3.5.3. **[Moments](/P/chi2-mom)** <br>
+   
+   3.6. Beta distribution <br>
+   &emsp;&ensp; 3.6.1. *[Definition](/D/beta)* <br>
+   &emsp;&ensp; 3.6.2. **[Probability density function](/P/beta-pdf)** <br>
+   
+   3.7. Wald distribution <br>
+   &emsp;&ensp; 3.7.1. *[Definition](/D/wald)* <br>
+   &emsp;&ensp; 3.7.2. **[Probability density function](/P/wald-pdf)** <br>
+   &emsp;&ensp; 3.7.3. **[Moment-generating function](/P/wald-mgf)** <br>
+   &emsp;&ensp; 3.7.4. **[Mean](/P/wald-mean)** <br>
+   &emsp;&ensp; 3.7.5. **[Variance](/P/wald-var)** <br>
 
 4. Multivariate continuous distributions
 

P/chi2-gam.md

@@ -38,6 +38,6 @@ If we let $\alpha = k/2$ and $\beta = 1/2$, we obtain
 
 $$ \label{eq:gam-pdf-chi2}
 \mathrm{Gam}\left(x; \frac{k}{2}, \frac{1}{2}\right) = \frac{x^{k/2-1} \, e^{-x/2}}{\Gamma(k/2) 2^{k/2}} = \frac{1}{2^{k/2} \Gamma(k/2)} \, x^{k/2-1} \, e^{-x/2}
-$$\
+$$
 
 which is equivalent to the [probability density function of the chi-square distribution](/P/chi2-pdf).