Merge pull request #39 from StatProofBook/master

update to master

Author: JoramSoch

D/rvar-uni.md

@@ -29,8 +29,8 @@ username: "JoramSoch"
 
 **Definition:** Let $X$ be a [random variable](/D/rvar) with possible outcomes $\mathcal{X}$. Then,
 
-* $X$ is called a univariate random variable or [random scalar](/D/rvar), if $\mathcal{X}$ is one-dimensional, i.e. (a subset of) the set of real numbers $\mathbb{R}$;
+* $X$ is called a univariate random variable or [random scalar](/D/rvar), if $\mathcal{X}$ is one-dimensional, i.e. (a subset of) the real numbers $\mathbb{R}$;
 
-* $X$ is called a multivariate random variable or [random vector](/D/rvec), if $\mathcal{X}$ is multi-dimensional, e.g. (a subset of) the set of real vectors $\mathbb{R}^n$;
+* $X$ is called a multivariate random variable or [random vector](/D/rvec), if $\mathcal{X}$ is multi-dimensional, e.g. (a subset of) the $n$-dimensional Euclidean space $\mathbb{R}^n$;
 
-* $X$ is called a matrix-valued random variable or [random matrix](/D/rmat), if $\mathcal{X}$ is (a subset of) the set of real matrices $\mathbb{R}^{n \times p}$.
+* $X$ is called a matrix-valued random variable or [random matrix](/D/rmat), if $\mathcal{X}$ is (a subset of) the set of $n \times p$ real matrices $\mathbb{R}^{n \times p}$.

I/Definition_by_Author.md

@@ -4,7 +4,7 @@ title: "Definition by Author"
 ---
 
 
-### JoramSoch (101 definitions)
+### JoramSoch (102 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Bayesian information criterion](/D/bic)
@@ -105,6 +105,7 @@ title: "Definition by Author"
 - [Standardized moment](/D/mom-stand)
 - [Statistical independence](/D/ind)
 - [Total sum of squares](/D/tss)
+- [Univariate and multivariate random variable](/D/rvar-uni)
 - [Variance](/D/var)
 - [Wishart distribution](/D/wish)
 

I/Definition_by_Number.md

@@ -112,3 +112,4 @@ title: "Definition by Number"
 | D103 | prob-exc | [Exceedance probability](/D/prob-exc) | JoramSoch | 2020-10-22 |
 | D104 | dir-data | [Dirichlet-distributed data](/D/dir-data) | JoramSoch | 2020-10-22 |
 | D105 | rvar-disc | [Discrete and continuous random variable](/D/rvar-disc) | JoramSoch | 2020-10-29 |
+| D106 | rvar-uni | [Univariate and multivariate random variable](/D/rvar-uni) | JoramSoch | 2020-11-06 |

I/Definition_by_Topic.md

@@ -158,6 +158,10 @@ title: "Definition by Topic"
 
 - [Total sum of squares](/D/tss)
 
+### U
+
+- [Univariate and multivariate random variable](/D/rvar-uni)
+
 ### V
 
 - [Variance](/D/var)

I/Proof_by_Author.md

@@ -4,7 +4,7 @@ title: "Proof by Author"
 ---
 
 
-### JoramSoch (176 proofs)
+### JoramSoch (179 proofs)
 
 - [(Non-)Multiplicativity of the expected value](/P/mean-mult)
 - [Additivity of the Kullback-Leibler divergence for independent distributions](/P/kl-add)
@@ -25,6 +25,7 @@ title: "Proof by Author"
 - [Convexity of the Kullback-Leibler divergence](/P/kl-conv)
 - [Convexity of the cross-entropy](/P/entcross-conv)
 - [Covariance of independent random variables](/P/cov-ind)
+- [Cumulative distribution function of a strictly decreasing function of a random variable](/P/cdf-sdfct)
 - [Cumulative distribution function of a strictly increasing function of a random variable](/P/cdf-sifct)
 - [Cumulative distribution function of the continuous uniform distribution](/P/cuni-cdf)
 - [Cumulative distribution function of the discrete uniform distribution](/P/duni-cdf)
@@ -42,7 +43,7 @@ title: "Proof by Author"
 - [Differential entropy of the multivariate normal distribution](/P/mvn-dent)
 - [Differential entropy of the normal distribution](/P/norm-dent)
 - [Equivalence of matrix-normal distribution and multivariate normal distribution](/P/matn-mvn)
-- [Exceedance probabilities for the the Dirichlet distribution](/P/dir-ep)
+- [Exceedance probabilities for the Dirichlet distribution](/P/dir-ep)
 - [Expectation of a quadratic form](/P/mean-qf)
 - [Expected value of a non-negative random variable](/P/mean-nnrvar)
 - [Expected value of x times ln(x) for a gamma distribution](/P/gam-xlogx)
@@ -128,6 +129,7 @@ title: "Proof by Author"
 - [Posterior model probability in terms of log Bayes factor](/P/pmp-lbf)
 - [Posterior probability of the alternative hypothesis for Bayesian linear regression](/P/blr-pp)
 - [Probability and log-odds in logistic regression](/P/logreg-pnlo)
+- [Probability density function of a strictly decreasing function of a continuous random variable](/P/pdf-sdfct)
 - [Probability density function of a strictly increasing function of a continuous random variable](/P/pdf-sifct)
 - [Probability density function of the Dirichlet distribution](/P/dir-pdf)
 - [Probability density function of the beta distribution](/P/beta-pdf)
@@ -138,6 +140,7 @@ title: "Proof by Author"
 - [Probability density function of the multivariate normal distribution](/P/mvn-pdf)
 - [Probability density function of the normal distribution](/P/norm-pdf)
 - [Probability density function of the normal-gamma distribution](/P/ng-pdf)
+- [Probability mass function of a strictly decreasing function of a discrete random variable](/P/pmf-sdfct)
 - [Probability mass function of a strictly increasing function of a discrete random variable](/P/pmf-sifct)
 - [Probability mass function of the Bernoulli distribution](/P/bern-pmf)
 - [Probability mass function of the Poisson distribution](/P/poiss-pmf)

I/Proof_by_Number.md

@@ -187,8 +187,11 @@ title: "Proof by Number"
 | P178 | gam-cdf | [Cumulative distribution function of the gamma distribution](/P/gam-cdf) | JoramSoch | 2020-10-15 |
 | P179 | gam-xlogx | [Expected value of x times ln(x) for a gamma distribution](/P/gam-xlogx) | JoramSoch | 2020-10-15 |
 | P180 | norm-snorm3 | [Relation between normal distribution and standard normal distribution](/P/norm-snorm3) | JoramSoch | 2020-10-22 |
-| P181 | dir-ep | [Exceedance probabilities for the the Dirichlet distribution](/P/dir-ep) | JoramSoch | 2020-10-22 |
+| P181 | dir-ep | [Exceedance probabilities for the Dirichlet distribution](/P/dir-ep) | JoramSoch | 2020-10-22 |
 | P182 | dir-mle | [Maximum likelihood estimation for Dirichlet-distributed data](/P/dir-mle) | JoramSoch | 2020-10-22 |
 | P183 | cdf-sifct | [Cumulative distribution function of a strictly increasing function of a random variable](/P/cdf-sifct) | JoramSoch | 2020-10-29 |
 | P184 | pmf-sifct | [Probability mass function of a strictly increasing function of a discrete random variable](/P/pmf-sifct) | JoramSoch | 2020-10-29 |
 | P185 | pdf-sifct | [Probability density function of a strictly increasing function of a continuous random variable](/P/pdf-sifct) | JoramSoch | 2020-10-29 |
+| P186 | cdf-sdfct | [Cumulative distribution function of a strictly decreasing function of a random variable](/P/cdf-sdfct) | JoramSoch | 2020-11-06 |
+| P187 | pmf-sdfct | [Probability mass function of a strictly decreasing function of a discrete random variable](/P/pmf-sdfct) | JoramSoch | 2020-11-06 |
+| P188 | pdf-sdfct | [Probability density function of a strictly decreasing function of a continuous random variable](/P/pdf-sdfct) | JoramSoch | 2020-11-06 |

I/Proof_by_Topic.md

@@ -35,6 +35,7 @@ title: "Proof by Topic"
 - [Convexity of the Kullback-Leibler divergence](/P/kl-conv)
 - [Convexity of the cross-entropy](/P/entcross-conv)
 - [Covariance of independent random variables](/P/cov-ind)
+- [Cumulative distribution function of a strictly decreasing function of a random variable](/P/cdf-sdfct)
 - [Cumulative distribution function of a strictly increasing function of a random variable](/P/cdf-sifct)
 - [Cumulative distribution function of the continuous uniform distribution](/P/cuni-cdf)
 - [Cumulative distribution function of the discrete uniform distribution](/P/duni-cdf)
@@ -59,7 +60,7 @@ title: "Proof by Topic"
 
 - [Encompassing Prior Method for computing Bayes Factors](/P/bf-ep)
 - [Equivalence of matrix-normal distribution and multivariate normal distribution](/P/matn-mvn)
-- [Exceedance probabilities for the the Dirichlet distribution](/P/dir-ep)
+- [Exceedance probabilities for the Dirichlet distribution](/P/dir-ep)
 - [Expectation of a quadratic form](/P/mean-qf)
 - [Expected value of a non-negative random variable](/P/mean-nnrvar)
 - [Expected value of x times ln(x) for a gamma distribution](/P/gam-xlogx)
@@ -178,6 +179,7 @@ title: "Proof by Topic"
 - [Posterior model probability in terms of log Bayes factor](/P/pmp-lbf)
 - [Posterior probability of the alternative hypothesis for Bayesian linear regression](/P/blr-pp)
 - [Probability and log-odds in logistic regression](/P/logreg-pnlo)
+- [Probability density function of a strictly decreasing function of a continuous random variable](/P/pdf-sdfct)
 - [Probability density function of a strictly increasing function of a continuous random variable](/P/pdf-sifct)
 - [Probability density function of the Dirichlet distribution](/P/dir-pdf)
 - [Probability density function of the Wald distribution](/P/wald-pdf)
@@ -189,6 +191,7 @@ title: "Proof by Topic"
 - [Probability density function of the multivariate normal distribution](/P/mvn-pdf)
 - [Probability density function of the normal distribution](/P/norm-pdf)
 - [Probability density function of the normal-gamma distribution](/P/ng-pdf)
+- [Probability mass function of a strictly decreasing function of a discrete random variable](/P/pmf-sdfct)
 - [Probability mass function of a strictly increasing function of a discrete random variable](/P/pmf-sifct)
 - [Probability mass function of the Bernoulli distribution](/P/bern-pmf)
 - [Probability mass function of the Poisson distribution](/P/poiss-pmf)

P/dir-ep.md

@@ -7,7 +7,7 @@ affiliation: "BCCN Berlin"
 e_mail: "joram.soch@bccn-berlin.de"
 date: 2020-10-22 08:04:00
 
-title: "Exceedance probabilities for the the Dirichlet distribution"
+title: "Exceedance probabilities for the Dirichlet distribution"
 chapter: "Probability Distributions"
 section: "Multivariate continuous distributions"
 topic: "Dirichlet distribution"