updated index pages

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

Author: JoramSoch

I/Definition_by_Author.md

@@ -4,7 +4,7 @@ title: "Definition by Author"
 ---
 
 
-### JoramSoch (93 definitions)
+### JoramSoch (96 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Bayesian information criterion](/D/bic)
@@ -15,6 +15,7 @@ title: "Definition by Author"
 - [Binomial distribution](/D/bin)
 - [Binomial observations](/D/bin-data)
 - [Categorical distribution](/D/cat)
+- [Central moment](/D/mom-cent)
 - [Coefficient of determination](/D/rsq)
 - [Conditional differential entropy](/D/dent-cond)
 - [Conditional entropy](/D/ent-cond)
@@ -88,13 +89,15 @@ title: "Definition by Author"
 - [Random matrix](/D/rmat)
 - [Random variable](/D/rvar)
 - [Random vector](/D/rvec)
+- [Raw moment](/D/mom-raw)
 - [Residual sum of squares](/D/rss)
 - [Residual variance](/D/resvar)
 - [Residual-forming matrix](/D/rfmat)
 - [Shannon entropy](/D/ent)
 - [Signal-to-noise ratio](/D/snr)
 - [Standard deviation](/D/std)
 - [Standard gamma distribution](/D/sgam)
+- [Standardized moment](/D/mom-stand)
 - [Statistical independence](/D/ind)
 - [Total sum of squares](/D/tss)
 - [Variance](/D/var)

I/Definition_by_Number.md

@@ -103,3 +103,6 @@ title: "Definition by Number"
 | D94 | std | [Standard deviation](/D/std) | JoramSoch | 2020-09-03 |
 | D95 | wald | [Wald distribution](/D/wald) | tomfaulkenberry | 2020-09-04 |
 | D96 | const | [Constant](/D/const) | JoramSoch | 2020-09-09 |
+| 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 |

I/Definition_by_Topic.md

@@ -22,6 +22,7 @@ title: "Definition by Topic"
 ### C
 
 - [Categorical distribution](/D/cat)
+- [Central moment](/D/mom-cent)
 - [Coefficient of determination](/D/rsq)
 - [Conditional differential entropy](/D/dent-cond)
 - [Conditional entropy](/D/ent-cond)
@@ -133,6 +134,7 @@ title: "Definition by Topic"
 - [Random matrix](/D/rmat)
 - [Random variable](/D/rvar)
 - [Random vector](/D/rvec)
+- [Raw moment](/D/mom-raw)
 - [Residual sum of squares](/D/rss)
 - [Residual variance](/D/resvar)
 - [Residual-forming matrix](/D/rfmat)
@@ -143,6 +145,7 @@ title: "Definition by Topic"
 - [Signal-to-noise ratio](/D/snr)
 - [Standard deviation](/D/std)
 - [Standard gamma distribution](/D/sgam)
+- [Standardized moment](/D/mom-stand)
 - [Statistical independence](/D/ind)
 
 ### T

I/Proof_by_Author.md

@@ -4,7 +4,7 @@ title: "Proof by Author"
 ---
 
 
-### JoramSoch (163 proofs)
+### JoramSoch (166 proofs)
 
 - [(Non-)Multiplicativity of the expected value](/P/mean-mult)
 - [Additivity of the Kullback-Leibler divergence for independent distributions](/P/kl-add)
@@ -45,6 +45,7 @@ title: "Proof by Author"
 - [Exponential distribution is a special case of gamma distribution](/P/exp-gam)
 - [Expression of the cumulative distribution function of the normal distribution without the error function](/P/norm-cdfwerf)
 - [First central moment is zero](/P/momcent-1st)
+- [First raw moment is mean](/P/momraw-1st)
 - [Full width at half maximum for the normal distribution](/P/norm-fwhm)
 - [Gibbs' inequality](/P/gibbs-ineq)
 - [Invariance of the Kullback-Leibler divergence under parameter transformation](/P/kl-inv)
@@ -156,8 +157,10 @@ title: "Proof by Author"
 - [Relationship between covariance and correlation](/P/cov-corr)
 - [Relationship between covariance matrix and correlation matrix](/P/covmat-corrmat)
 - [Relationship between precision matrix and correlation matrix](/P/precmat-corrmat)
+- [Relationship between second raw moment, variance and mean](/P/momraw-2nd)
 - [Relationship between signal-to-noise ratio and R²](/P/snr-rsq)
 - [Scaling of the variance upon multiplication with a constant](/P/var-scal)
+- [Second central moment is variance](/P/momcent-2nd)
 - [Transformation matrices for ordinary least squares](/P/mlr-mat)
 - [Transposition of a matrix-normal random variable](/P/matn-trans)
 - [Variance of constant is zero](/P/var-const)

I/Proof_by_Number.md

@@ -177,3 +177,6 @@ title: "Proof by Number"
 | P168 | wald-mgf | [Moment-generating function of the Wald distribution](/P/wald-mgf) | tomfaulkenberry | 2020-09-13 |
 | P169 | wald-mean | [Mean of the Wald distribution](/P/wald-mean) | tomfaulkenberry | 2020-09-13 |
 | P170 | wald-var | [Variance of the Wald distribution](/P/wald-var) | tomfaulkenberry | 2020-09-13 |
+| 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 |

I/Proof_by_Topic.md

@@ -64,6 +64,7 @@ title: "Proof by Topic"
 ### F
 
 - [First central moment is zero](/P/momcent-1st)
+- [First raw moment is mean](/P/momraw-1st)
 - [Full width at half maximum for the normal distribution](/P/norm-fwhm)
 
 ### G
@@ -212,12 +213,14 @@ title: "Proof by Topic"
 - [Relationship between covariance and correlation](/P/cov-corr)
 - [Relationship between covariance matrix and correlation matrix](/P/covmat-corrmat)
 - [Relationship between precision matrix and correlation matrix](/P/precmat-corrmat)
+- [Relationship between second raw moment, variance and mean](/P/momraw-2nd)
 - [Relationship between signal-to-noise ratio and R²](/P/snr-rsq)
 
 ### S
 
 - [Savage-Dickey Density Ratio for computing Bayes Factors](/P/bf-sddr)
 - [Scaling of the variance upon multiplication with a constant](/P/var-scal)
+- [Second central moment is variance](/P/momcent-2nd)
 
 ### T
 

I/Proofs_without_Source.md

@@ -14,6 +14,7 @@ title: "Proofs without Source"
 - [Derivation of the log model evidence](/P/lme-der)
 - [Derivation of the posterior model probability](/P/pmp-der)
 - [Exponential distribution is a special case of gamma distribution](/P/exp-gam)
+- [First raw moment is mean](/P/momraw-1st)
 - [Joint likelihood is the product of likelihood function and prior density](/P/jl-lfnprior)
 - [Linear transformation theorem for the matrix-normal distribution](/P/matn-ltt)
 - [Log model evidence for multinomial observations](/P/mult-lme)
@@ -60,6 +61,7 @@ title: "Proofs without Source"
 - [Relationship between R² and maximum log-likelihood](/P/rsq-mll)
 - [Relationship between covariance and correlation](/P/cov-corr)
 - [Relationship between precision matrix and correlation matrix](/P/precmat-corrmat)
+- [Relationship between second raw moment, variance and mean](/P/momraw-2nd)
 - [Relationship between signal-to-noise ratio and R²](/P/snr-rsq)
 - [Transitivity of Bayes Factors](/P/bf-trans)
 - [Transposition of a matrix-normal random variable](/P/matn-trans)