Merge pull request #92 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 (315 proofs)
+### JoramSoch (321 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -44,6 +44,7 @@ title: "Proof by Author"
 - [Corrected Akaike information criterion in terms of maximum log-likelihood](/P/aicc-mll)
 - [Correlation always falls between -1 and +1](/P/corr-range)
 - [Correlation coefficient in terms of standard scores](/P/corr-z)
+- [Covariance matrix of the categorical distribution](/P/cat-cov)
 - [Covariance of independent random variables](/P/cov-ind)
 - [Cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbf)
 - [Cross-validated log model evidence for the univariate Gaussian with known variance](/P/ugkv-cvlme)
@@ -77,6 +78,10 @@ title: "Proof by Author"
 - [Distribution of the transformed general linear model](/P/tglm-dist)
 - [Distributional transformation using cumulative distribution function](/P/cdf-dt)
 - [Effects of mean-centering on parameter estimates for simple linear regression](/P/slr-meancent)
+- [Entropy of the Bernoulli distribution](/P/bern-ent)
+- [Entropy of the binomial distribution](/P/bin-ent)
+- [Entropy of the categorical distribution](/P/cat-ent)
+- [Entropy of the multinomial distribution](/P/mult-ent)
 - [Equivalence of matrix-normal distribution and multivariate normal distribution](/P/matn-mvn)
 - [Equivalence of parameter estimates from the transformed general linear model](/P/tglm-para)
 - [Exceedance probabilities for the Dirichlet distribution](/P/dir-ep)
@@ -236,6 +241,7 @@ title: "Proof by Author"
 - [Probability density function of the gamma distribution](/P/gam-pdf)
 - [Probability density function of the matrix-normal distribution](/P/matn-pdf)
 - [Probability density function of the multivariate normal distribution](/P/mvn-pdf)
+- [Probability density function of the multivariate t-distribution](/P/mvt-pdf)
 - [Probability density function of the normal distribution](/P/norm-pdf)
 - [Probability density function of the normal-gamma distribution](/P/ng-pdf)
 - [Probability density function of the normal-Wishart distribution](/P/nw-pdf)

I/PbN.md

@@ -338,3 +338,9 @@ title: "Proof by Number"
 | 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 |
+| P333 | mvt-pdf | [Probability density function of the multivariate t-distribution](/P/mvt-pdf) | JoramSoch | 2022-09-02 |
+| P334 | bern-ent | [Entropy of the Bernoulli distribution](/P/bern-ent) | JoramSoch | 2022-09-02 |
+| P335 | bin-ent | [Entropy of the binomial distribution](/P/bin-ent) | JoramSoch | 2022-09-02 |
+| P336 | cat-ent | [Entropy of the categorical distribution](/P/cat-ent) | JoramSoch | 2022-09-09 |
+| P337 | mult-ent | [Entropy of the multinomial distribution](/P/mult-ent) | JoramSoch | 2022-09-09 |
+| P338 | cat-cov | [Covariance matrix of the categorical distribution](/P/cat-cov) | JoramSoch | 2022-09-09 |

I/PbT.md

@@ -47,6 +47,7 @@ title: "Proof by Topic"
 - [Corrected Akaike information criterion in terms of maximum log-likelihood](/P/aicc-mll)
 - [Correlation always falls between -1 and +1](/P/corr-range)
 - [Correlation coefficient in terms of standard scores](/P/corr-z)
+- [Covariance matrix of the categorical distribution](/P/cat-cov)
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 - [Covariance of independent random variables](/P/cov-ind)
 - [Cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbf)
@@ -89,6 +90,10 @@ title: "Proof by Topic"
 
 - [Effects of mean-centering on parameter estimates for simple linear regression](/P/slr-meancent)
 - [Encompassing Prior Method for computing Bayes Factors](/P/bf-ep)
+- [Entropy of the Bernoulli distribution](/P/bern-ent)
+- [Entropy of the binomial distribution](/P/bin-ent)
+- [Entropy of the categorical distribution](/P/cat-ent)
+- [Entropy of the multinomial distribution](/P/mult-ent)
 - [Equivalence of matrix-normal distribution and multivariate normal distribution](/P/matn-mvn)
 - [Equivalence of parameter estimates from the transformed general linear model](/P/tglm-para)
 - [Exceedance probabilities for the Dirichlet distribution](/P/dir-ep)
@@ -285,6 +290,7 @@ title: "Proof by Topic"
 - [Probability density function of the log-normal distribution](/P/lognorm-pdf)
 - [Probability density function of the matrix-normal distribution](/P/matn-pdf)
 - [Probability density function of the multivariate normal distribution](/P/mvn-pdf)
+- [Probability density function of the multivariate t-distribution](/P/mvt-pdf)
 - [Probability density function of the normal distribution](/P/norm-pdf)
 - [Probability density function of the normal-gamma distribution](/P/ng-pdf)
 - [Probability density function of the normal-Wishart distribution](/P/nw-pdf)

I/PwS.md

@@ -9,6 +9,7 @@ title: "Proofs without Source"
 - [Bayesian information criterion for multiple linear regression](/P/mlr-bic)
 - [Chi-squared distribution is a special case of gamma distribution](/P/chi2-gam)
 - [Conditional distributions of the normal-gamma distribution](/P/ng-cond)
+- [Covariance matrix of the categorical distribution](/P/cat-cov)
 - [Cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbf)
 - [Cross-validated log model evidence for the univariate Gaussian with known variance](/P/ugkv-cvlme)
 - [Cumulative distribution function in terms of probability density function of a continuous random variable](/P/cdf-pdf)
@@ -25,6 +26,9 @@ title: "Proofs without Source"
 - [Deviance information criterion for multiple linear regression](/P/blr-dic)
 - [Differential entropy of the normal-gamma distribution](/P/ng-dent)
 - [Effects of mean-centering on parameter estimates for simple linear regression](/P/slr-meancent)
+- [Entropy of the binomial distribution](/P/bin-ent)
+- [Entropy of the categorical distribution](/P/cat-ent)
+- [Entropy of the multinomial distribution](/P/mult-ent)
 - [Expectation of the cross-validated log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-cvlbfmean)
 - [Expectation of the log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-lbfmean)
 - [Exponential distribution is a special case of gamma distribution](/P/exp-gam)
@@ -78,6 +82,7 @@ title: "Proofs without Source"
 - [Probability density function of the gamma distribution](/P/gam-pdf)
 - [Probability density function of the matrix-normal distribution](/P/matn-pdf)
 - [Probability density function of the multivariate normal distribution](/P/mvn-pdf)
+- [Probability density function of the multivariate t-distribution](/P/mvt-pdf)
 - [Probability density function of the normal distribution](/P/norm-pdf)
 - [Probability density function of the normal-Wishart distribution](/P/nw-pdf)
 - [Probability density function of the Wald distribution](/P/wald-pdf)