Merge pull request #120 from StatProofBook/master

update to master

Author: JoramSoch

I/DbA.md

@@ -8,7 +8,7 @@ title: "Definition by Author"
 
 - [Sample covariance](/D/cov-samp)
 
-### JoramSoch (181 definitions)
+### JoramSoch (182 definitions)
 
 - [Akaike information criterion](/D/aic)
 - [Alternative hypothesis](/D/h1)
@@ -101,6 +101,7 @@ title: "Definition by Author"
 - [Maximum entropy prior distribution](/D/prior-maxent)
 - [Maximum likelihood estimation](/D/mle)
 - [Maximum log-likelihood](/D/mll)
+- [Maximum-a-posteriori estimation](/D/map)
 - [Mean squared error](/D/mse)
 - [Median](/D/med)
 - [Method-of-moments estimation](/D/mome)

I/DbN.md

@@ -197,3 +197,4 @@ title: "Definition by Number"
 | D188 | skew | [Skewness](/D/skew) | tomfaulkenberry | 2023-04-20 |
 | D189 | bvn | [Bivariate normal distribution](/D/bvn) | JoramSoch | 2023-09-22 |
 | D190 | skew-samp | [Sample skewness](/D/skew-samp) | tomfaulkenberry | 2023-10-30 |
+| D191 | map | [Maximum-a-posteriori estimation](/D/map) | JoramSoch | 2023-12-01 |

I/DbT.md

@@ -136,6 +136,7 @@ title: "Definition by Topic"
 - [Maximum entropy prior distribution](/D/prior-maxent)
 - [Maximum likelihood estimation](/D/mle)
 - [Maximum log-likelihood](/D/mll)
+- [Maximum-a-posteriori estimation](/D/map)
 - [Mean squared error](/D/mse)
 - [Median](/D/med)
 - [Method-of-moments estimation](/D/mome)

I/PbA.md

@@ -8,7 +8,7 @@ title: "Proof by Author"
 
 - [Covariance matrix of the multinomial distribution](/P/mult-cov)
 
-### JoramSoch (395 proofs)
+### JoramSoch (396 proofs)
 
 - [Accuracy and complexity for the univariate Gaussian](/P/ug-anc)
 - [Accuracy and complexity for the univariate Gaussian with known variance](/P/ugkv-anc)
@@ -198,6 +198,7 @@ title: "Proof by Author"
 - [Maximum log-likelihood for binomial observations](/P/bin-mll)
 - [Maximum log-likelihood for multinomial observations](/P/mult-mll)
 - [Maximum log-likelihood for multiple linear regression](/P/mlr-mll)
+- [Maximum-a-posteriori estimation for binomial observations](/P/bin-map)
 - [Mean of the Bernoulli distribution](/P/bern-mean)
 - [Mean of the beta distribution](/P/beta-mean)
 - [Mean of the binomial distribution](/P/bin-mean)

I/PbN.md

@@ -432,3 +432,4 @@ title: "Proof by Number"
 | P424 | exg-mome | [Method of moments for ex-Gaussian-distributed data](/P/exg-mome) | tomfaulkenberry | 2023-10-30 |
 | P425 | duni-kl | [Kullback-Leibler divergence for the discrete uniform distribution](/P/duni-kl) | JoramSoch | 2023-11-17 |
 | 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 |

I/PbT.md

@@ -231,6 +231,7 @@ title: "Proof by Topic"
 - [Maximum log-likelihood for binomial observations](/P/bin-mll)
 - [Maximum log-likelihood for multinomial observations](/P/mult-mll)
 - [Maximum log-likelihood for multiple linear regression](/P/mlr-mll)
+- [Maximum-a-posteriori estimation for binomial observations](/P/bin-map)
 - [Mean of the Bernoulli distribution](/P/bern-mean)
 - [Mean of the beta distribution](/P/beta-mean)
 - [Mean of the binomial distribution](/P/bin-mean)

I/PwS.md

@@ -75,6 +75,7 @@ title: "Proofs without Source"
 - [Maximum likelihood estimation for the Poisson distribution with exposure values](/P/poissexp-mle)
 - [Maximum log-likelihood for binomial observations](/P/bin-mll)
 - [Maximum log-likelihood for multinomial observations](/P/mult-mll)
+- [Maximum-a-posteriori estimation for binomial observations](/P/bin-map)
 - [Mean of the categorical distribution](/P/cat-mean)
 - [Mean of the continuous uniform distribution](/P/cuni-mean)
 - [Mean of the ex-Gaussian distribution](/P/exg-mean)

P/pdf-sdfct.md

@@ -45,7 +45,7 @@ $$ \label{eq:Y-range}
 $$
 
 
-**Proof:** The [cumulative distribution function of a strictly decreasing function](/P/cdf-sifct) is
+**Proof:** The [cumulative distribution function of a strictly decreasing function](/P/cdf-sdfct) is
 
 $$ \label{eq:cdf-sdfct}
 F_Y(y) = \left\{

P/t-pdf.md

@@ -87,7 +87,7 @@ J &= \left[ \begin{matrix}
 \frac{\mathrm{d}Y}{\mathrm{d}T} & \frac{\mathrm{d}Y}{\mathrm{d}W}
 \end{matrix} \right]
 = \left[ \begin{matrix}
-\sqrt{\frac{W}{\nu}} & \frac{T}{2 \sqrt{W/\nu}} \\
+\sqrt{\frac{W}{\nu}} & \frac{T}{2 \nu \sqrt{W/\nu}} \\
 0 & 1
 \end{matrix} \right] \\
 \lvert J \rvert  &= \sqrt{\frac{W}{\nu}} \; .