Merge pull request #122 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 (397 proofs)
+### JoramSoch (398 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -25,6 +25,7 @@ title: "Proof by Author"
 - [Bayesian information criterion for multiple linear regression](/P/mlr-bic)
 - [Bayesian model averaging in terms of log model evidences](/P/bma-lme)
 - [Best linear unbiased estimator for the inverse general linear model](/P/iglm-blue)
+- [Binomial test](/P/bin-test)
 - [Characteristic function of a function of a random variable](/P/cf-fct)
 - [Combined posterior distributions in terms of individual posterior distributions obtained from conditionally independent data](/P/post-ind)
 - [Concavity of the Shannon entropy](/P/ent-conc)

I/PbN.md

@@ -434,3 +434,4 @@ title: "Proof by Number"
 | P426 | gam-scal | [Scaling of a random variable following the gamma distribution](/P/gam-scal) | JoramSoch | 2023-11-24 |
 | P427 | bin-map | [Maximum-a-posteriori estimation for binomial observations](/P/bin-map) | JoramSoch | 2023-12-01 |
 | P428 | mult-map | [Maximum-a-posteriori estimation for multinomial observations](/P/mult-map) | JoramSoch | 2023-12-08 |
+| P429 | bin-test | [Binomial test](/P/bin-test) | JoramSoch | 2023-12-16 |

I/PbT.md

@@ -24,6 +24,7 @@ title: "Proof by Topic"
 - [Bayesian information criterion for multiple linear regression](/P/mlr-bic)
 - [Bayesian model averaging in terms of log model evidences](/P/bma-lme)
 - [Best linear unbiased estimator for the inverse general linear model](/P/iglm-blue)
+- [Binomial test](/P/bin-test)
 
 ### C
 

P/bin-test.md

@@ -92,7 +92,7 @@ $$ \label{eq:y-cvals}
 \end{split}
 $$
 
-Given the test statistic's CDF in \eqref{eq:y-cdf}, this is fulfilled by the values $c_1$ and $c_2$ defined in \eqref{eq:bin-test-c1} and \eqref{eq:bin-test-c2}. Thus, the null hypothesis $H_0$ [can be rejected](/D/cval), if the [observed test statistic](/D/test) is inside the rejection region:
+Given the test statistic's CDF in \eqref{eq:y-cdf}, this is fulfilled by the values $c_1$ and $c_2$ defined in \eqref{eq:bin-test-c1} and \eqref{eq:bin-test-c2}. Thus, the null hypothesis $H_0$ [can be rejected](/D/cval), if the [observed test statistic is inside the rejection region](/D/test):
 
 $$ \label{eq:bin-test-rej-qed}
 y \in \left\lbrace 0, \ldots, c_1 \right\rbrace \cup \left\lbrace c_2, \ldots, n \right\rbrace \; .

P/dent-addvec.md

@@ -14,6 +14,12 @@ topic: "Differential entropy"
 theorem: "Addition upon matrix multiplication"
 
 sources:
+  - authors: "Cover, Thomas M. & Thomas, Joy A."
+    year: 1991
+    title: "Properties of Differential Entropy, Relative Entropy, and Mutual Information"
+    in: "Elements of Information Theory"
+    pages: "sect. 8.6, p. 253"
+    url: "https://www.google.de/books/edition/Elements_of_Information_Theory/j0DBDwAAQBAJ"
   - authors: "Wikipedia"
     year: 2021
     title: "Differential entropy"

P/prob-tot.md

@@ -20,12 +20,6 @@ sources:
     in: "Kendall's Advanced Theory of Statistics, Vol. 1: Distribution Theory"
     pages: "p. 288, eq. (d); p. 289, eq. 8.7"
     url: "https://www.wiley.com/en-us/Kendall%27s+Advanced+Theory+of+Statistics%2C+3+Volumes%2C+Set%2C+6th+Edition-p-9780470669549"
-  - authors: "Alan Stuart & J. Keith Ord"
-    year: 1994
-    title: "Probability and Statistical Inference"
-    in: "Kendall's Advanced Theory of Statistics, Vol. 1: Distribution Theory"
-    pages: "ch. 8.6, p. 289, eq. 8.7"
-    url: "https://www.wiley.com/en-us/Kendall%27s+Advanced+Theory+of+Statistics%2C+3+Volumes%2C+Set%2C+6th+Edition-p-9780470669549"
   - authors: "Wikipedia"
     year: 2021
     title: "Law of total probability"