corrected index pages

The alphabetical ordering of "Definition by Topic" and "Proof by Topic" has been corrected, ensuring correct alphabetical order at every position.

Author: JoramSoch

I/DbT.md

@@ -58,10 +58,10 @@ title: "Definition by Topic"
 
 ### E
 
+- [Empirical and theoretical prior distribution](/D/prior-emp)
 - [Empirical Bayes](/D/eb)
 - [Empirical Bayes prior distribution](/D/prior-eb)
 - [Empirical Bayesian log model evidence](/D/eblme)
-- [Empirical and theoretical prior distribution](/D/prior-emp)
 - [Encompassing model](/D/encm)
 - [Estimation matrix](/D/emat)
 - [Exceedance probability](/D/prob-exc)
@@ -220,9 +220,9 @@ title: "Definition by Topic"
 
 - [Uniform and non-uniform prior distribution](/D/prior-uni)
 - [Uniform-prior log model evidence](/D/uplme)
+- [Univariate and multivariate random variable](/D/rvar-uni)
 - [Univariate Gaussian](/D/ug)
 - [Univariate Gaussian with known variance](/D/ugkv)
-- [Univariate and multivariate random variable](/D/rvar-uni)
 
 ### V
 

I/PbT.md

@@ -29,17 +29,17 @@ title: "Proof by Topic"
 - [Conditional distributions of the multivariate normal distribution](/P/mvn-cond)
 - [Conditional distributions of the normal-gamma distribution](/P/ng-cond)
 - [Conjugate prior distribution for Bayesian linear regression](/P/blr-prior)
-- [Conjugate prior distribution for Poisson-distributed data](/P/poiss-prior)
 - [Conjugate prior distribution for binomial observations](/P/bin-prior)
 - [Conjugate prior distribution for multinomial observations](/P/mult-prior)
 - [Conjugate prior distribution for multivariate Bayesian linear regression](/P/mblr-prior)
+- [Conjugate prior distribution for Poisson-distributed data](/P/poiss-prior)
 - [Conjugate prior distribution for the Poisson distribution with exposure values](/P/poissexp-prior)
 - [Conjugate prior distribution for the univariate Gaussian](/P/ug-prior)
 - [Conjugate prior distribution for the univariate Gaussian with known variance](/P/ugkv-prior)
 - [Construction of confidence intervals using Wilks' theorem](/P/ci-wilks)
 - [Construction of unbiased estimator for variance](/P/resvar-unb)
-- [Convexity of the Kullback-Leibler divergence](/P/kl-conv)
 - [Convexity of the cross-entropy](/P/entcross-conv)
+- [Convexity of the Kullback-Leibler divergence](/P/kl-conv)
 - [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)
@@ -105,8 +105,8 @@ title: "Proof by Topic"
 ### I
 
 - [Inflection points of the probability density function of the normal distribution](/P/norm-infl)
-- [Invariance of the Kullback-Leibler divergence under parameter transformation](/P/kl-inv)
 - [Invariance of the differential entropy under addition of a constant](/P/dent-inv)
+- [Invariance of the Kullback-Leibler divergence under parameter transformation](/P/kl-inv)
 - [Invariance of the variance under addition of a constant](/P/var-inv)
 - [Inverse transformation method using cumulative distribution function](/P/cdf-itm)
 
@@ -134,10 +134,10 @@ title: "Proof by Topic"
 - [Log Bayes factor in terms of log model evidences](/P/lbf-lme)
 - [Log family evidences in terms of log model evidences](/P/lfe-lme)
 - [Log model evidence for Bayesian linear regression](/P/blr-lme)
-- [Log model evidence for Poisson-distributed data](/P/poiss-lme)
 - [Log model evidence for binomial observations](/P/bin-lme)
 - [Log model evidence for multinomial observations](/P/mult-lme)
 - [Log model evidence for multivariate Bayesian linear regression](/P/mblr-lme)
+- [Log model evidence for Poisson-distributed data](/P/poiss-lme)
 - [Log model evidence for the Poisson distribution with exposure values](/P/poissexp-lme)
 - [Log model evidence for the univariate Gaussian](/P/ug-lme)
 - [Log model evidence for the univariate Gaussian with known variance](/P/ugkv-lme)
@@ -151,16 +151,14 @@ title: "Proof by Topic"
 - [Marginal distributions of the normal-gamma distribution](/P/ng-marg)
 - [Marginal likelihood is a definite integral of joint likelihood](/P/ml-jl)
 - [Maximum likelihood estimation for Dirichlet-distributed data](/P/dir-mle)
-- [Maximum likelihood estimation for Poisson-distributed data](/P/poiss-mle)
 - [Maximum likelihood estimation for multiple linear regression](/P/mlr-mle)
-- [Maximum likelihood estimation for the Poisson distribution with exposure values](/P/poissexp-mle)
+- [Maximum likelihood estimation for Poisson-distributed data](/P/poiss-mle)
 - [Maximum likelihood estimation for the general linear model](/P/glm-mle)
+- [Maximum likelihood estimation for the Poisson distribution with exposure values](/P/poissexp-mle)
 - [Maximum likelihood estimation for the univariate Gaussian](/P/ug-mle)
 - [Maximum likelihood estimation for the univariate Gaussian with known variance](/P/ugkv-mle)
 - [Maximum likelihood estimator of variance is biased](/P/resvar-bias)
 - [Mean of the Bernoulli distribution](/P/bern-mean)
-- [Mean of the Poisson distribution](/P/poiss-mean)
-- [Mean of the Wald distribution](/P/wald-mean)
 - [Mean of the beta distribution](/P/beta-mean)
 - [Mean of the binomial distribution](/P/bin-mean)
 - [Mean of the categorical distribution](/P/cat-mean)
@@ -170,6 +168,8 @@ title: "Proof by Topic"
 - [Mean of the multinomial distribution](/P/mult-mean)
 - [Mean of the normal distribution](/P/norm-mean)
 - [Mean of the normal-gamma distribution](/P/ng-mean)
+- [Mean of the Poisson distribution](/P/poiss-mean)
+- [Mean of the Wald distribution](/P/wald-mean)
 - [Median of the continuous uniform distribution](/P/cuni-med)
 - [Median of the exponential distribution](/P/exp-med)
 - [Median of the normal distribution](/P/norm-med)
@@ -180,22 +180,22 @@ title: "Proof by Topic"
 - [Moment in terms of moment-generating function](/P/mom-mgf)
 - [Moment-generating function of a function of a random variable](/P/mgf-fct)
 - [Moment-generating function of linear combination of independent random variables](/P/mgf-lincomb)
-- [Moment-generating function of the Wald distribution](/P/wald-mgf)
 - [Moment-generating function of the beta distribution](/P/beta-mgf)
 - [Moment-generating function of the normal distribution](/P/norm-mgf)
+- [Moment-generating function of the Wald distribution](/P/wald-mgf)
 - [Moments of the chi-squared distribution](/P/chi2-mom)
 - [Monotonicity of probability](/P/prob-mon)
 - [Monotonicity of the expected value](/P/mean-mono)
 
 ### N
 
 - [Necessary and sufficient condition for independence of multivariate normal random variables](/P/mvn-ind)
-- [(Non-)Multiplicativity of the expected value](/P/mean-mult)
 - [Non-invariance of the differential entropy under change of variables](/P/dent-noninv)
+- [(Non-)Multiplicativity of the expected value](/P/mean-mult)
+- [Non-negativity of the expected value](/P/mean-nonneg)
 - [Non-negativity of the Kullback-Leibler divergence](/P/kl-nonneg)
 - [Non-negativity of the Kullback-Leibler divergence](/P/kl-nonneg2)
 - [Non-negativity of the Shannon entropy](/P/ent-nonneg)
-- [Non-negativity of the expected value](/P/mean-nonneg)
 - [Non-negativity of the variance](/P/var-nonneg)
 - [Non-symmetry of the Kullback-Leibler divergence](/P/kl-nonsymm)
 - [Normal distribution maximizes differential entropy for fixed variance](/P/norm-maxent)
@@ -223,10 +223,10 @@ title: "Proof by Topic"
 - [Posterior credibility region against the omnibus null hypothesis for Bayesian linear regression](/P/blr-pcr)
 - [Posterior density is proportional to joint likelihood](/P/post-jl)
 - [Posterior distribution for Bayesian linear regression](/P/blr-post)
-- [Posterior distribution for Poisson-distributed data](/P/poiss-post)
 - [Posterior distribution for binomial observations](/P/bin-post)
 - [Posterior distribution for multinomial observations](/P/mult-post)
 - [Posterior distribution for multivariate Bayesian linear regression](/P/mblr-post)
+- [Posterior distribution for Poisson-distributed data](/P/poiss-post)
 - [Posterior distribution for the Poisson distribution with exposure values](/P/poissexp-post)
 - [Posterior distribution for the univariate Gaussian](/P/ug-post)
 - [Posterior distribution for the univariate Gaussian with known variance](/P/ugkv-post)
@@ -241,30 +241,30 @@ title: "Proof by Topic"
 - [Probability density function of a strictly increasing function of a continuous random variable](/P/pdf-sifct)
 - [Probability density function of a sum of independent discrete random variables](/P/pdf-sumind)
 - [Probability density function of an invertible function of a continuous random vector](/P/pdf-invfct)
-- [Probability density function of the Dirichlet distribution](/P/dir-pdf)
-- [Probability density function of the F-distribution](/P/f-pdf)
-- [Probability density function of the Wald distribution](/P/wald-pdf)
 - [Probability density function of the beta distribution](/P/beta-pdf)
 - [Probability density function of the chi-squared distribution](/P/chi2-pdf)
 - [Probability density function of the continuous uniform distribution](/P/cuni-pdf)
+- [Probability density function of the Dirichlet distribution](/P/dir-pdf)
 - [Probability density function of the exponential distribution](/P/exp-pdf)
+- [Probability density function of the F-distribution](/P/f-pdf)
 - [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 normal distribution](/P/norm-pdf)
 - [Probability density function of the normal-gamma distribution](/P/ng-pdf)
 - [Probability density function of the t-distribution](/P/t-pdf)
+- [Probability density function of the Wald distribution](/P/wald-pdf)
 - [Probability integral transform using cumulative distribution function](/P/cdf-pit)
 - [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 a sum of independent discrete random variables](/P/pmf-sumind)
 - [Probability mass function of an invertible function of a random vector](/P/pmf-invfct)
 - [Probability mass function of the Bernoulli distribution](/P/bern-pmf)
-- [Probability mass function of the Poisson distribution](/P/poiss-pmf)
 - [Probability mass function of the binomial distribution](/P/bin-pmf)
 - [Probability mass function of the categorical distribution](/P/cat-pmf)
 - [Probability mass function of the discrete uniform distribution](/P/duni-pmf)
 - [Probability mass function of the multinomial distribution](/P/mult-pmf)
+- [Probability mass function of the Poisson distribution](/P/poiss-pmf)
 - [Probability of exhaustive events](/P/prob-exh)
 - [Probability of the complement](/P/prob-comp)
 - [Probability of the empty set](/P/prob-emp)
@@ -285,15 +285,14 @@ title: "Proof by Topic"
 ### R
 
 - [Range of probability](/P/prob-range)
-- [Relation of Kullback-Leibler divergence to entropy](/P/kl-ent)
 - [Relation of continuous Kullback-Leibler divergence to differential entropy](/P/kl-dent)
 - [Relation of continuous mutual information to joint and conditional differential entropy](/P/cmi-jcde)
 - [Relation of continuous mutual information to marginal and conditional differential entropy](/P/cmi-mcde)
 - [Relation of continuous mutual information to marginal and joint differential entropy](/P/cmi-mjde)
+- [Relation of Kullback-Leibler divergence to entropy](/P/kl-ent)
 - [Relation of mutual information to joint and conditional entropy](/P/dmi-jce)
 - [Relation of mutual information to marginal and conditional entropy](/P/dmi-mce)
 - [Relation of mutual information to marginal and joint entropy](/P/dmi-mje)
-- [Relationship between R² and maximum log-likelihood](/P/rsq-mll)
 - [Relationship between coefficient of determination and correlation coefficient in simple linear regression](/P/slr-rsq)
 - [Relationship between correlation coefficient and slope estimate in simple linear regression](/P/slr-corr)
 - [Relationship between covariance and correlation](/P/cov-corr)
@@ -308,6 +307,7 @@ title: "Proof by Topic"
 - [Relationship between normal distribution and standard normal distribution](/P/norm-snorm3)
 - [Relationship between normal distribution and t-distribution](/P/norm-t)
 - [Relationship between precision matrix and correlation matrix](/P/precmat-corrmat)
+- [Relationship between R² and maximum log-likelihood](/P/rsq-mll)
 - [Relationship between residual variance and sample variance in simple linear regression](/P/slr-resvar)
 - [Relationship between second raw moment, variance and mean](/P/momraw-2nd)
 - [Relationship between signal-to-noise ratio and R²](/P/snr-rsq)
@@ -333,13 +333,13 @@ title: "Proof by Topic"
 
 - [Variance of constant is zero](/P/var-const)
 - [Variance of parameter estimates for simple linear regression](/P/slr-olsvar)
-- [Variance of the Poisson distribution](/P/poiss-var)
-- [Variance of the Wald distribution](/P/wald-var)
 - [Variance of the beta distribution](/P/beta-var)
 - [Variance of the gamma distribution](/P/gam-var)
 - [Variance of the linear combination of two random variables](/P/var-lincomb)
 - [Variance of the normal distribution](/P/norm-var)
+- [Variance of the Poisson distribution](/P/poiss-var)
 - [Variance of the sum of two random variables](/P/var-sum)
+- [Variance of the Wald distribution](/P/wald-var)
 
 ### W
 

I/PwS.md

@@ -31,23 +31,23 @@ title: "Proofs without Source"
 - [Linear combination of independent normal random variables](/P/norm-lincomb)
 - [Linear transformation theorem for the matrix-normal distribution](/P/matn-ltt)
 - [Log Bayes factor for the univariate Gaussian with known variance](/P/ugkv-lbf)
-- [Log model evidence for Poisson-distributed data](/P/poiss-lme)
 - [Log model evidence for multinomial observations](/P/mult-lme)
 - [Log model evidence for multivariate Bayesian linear regression](/P/mblr-lme)
+- [Log model evidence for Poisson-distributed data](/P/poiss-lme)
 - [Log model evidence for the Poisson distribution with exposure values](/P/poissexp-lme)
 - [Log model evidence for the univariate Gaussian with known variance](/P/ugkv-lme)
 - [Marginal distributions of the multivariate normal distribution](/P/mvn-marg)
 - [Marginal distributions of the normal-gamma distribution](/P/ng-marg)
 - [Marginal likelihood is a definite integral of joint likelihood](/P/ml-jl)
-- [Maximum likelihood estimation for Poisson-distributed data](/P/poiss-mle)
 - [Maximum likelihood estimation for multiple linear regression](/P/mlr-mle)
-- [Maximum likelihood estimation for the Poisson distribution with exposure values](/P/poissexp-mle)
+- [Maximum likelihood estimation for Poisson-distributed data](/P/poiss-mle)
 - [Maximum likelihood estimation for the general linear model](/P/glm-mle)
-- [Mean of the Wald distribution](/P/wald-mean)
+- [Maximum likelihood estimation for the Poisson distribution with exposure values](/P/poissexp-mle)
 - [Mean of the categorical distribution](/P/cat-mean)
 - [Mean of the continuous uniform distribution](/P/cuni-mean)
 - [Mean of the multinomial distribution](/P/mult-mean)
 - [Mean of the normal-gamma distribution](/P/ng-mean)
+- [Mean of the Wald distribution](/P/wald-mean)
 - [Median of the continuous uniform distribution](/P/cuni-med)
 - [Median of the exponential distribution](/P/exp-med)
 - [Median of the normal distribution](/P/norm-med)
@@ -57,25 +57,24 @@ title: "Proofs without Source"
 - [Necessary and sufficient condition for independence of multivariate normal random variables](/P/mvn-ind)
 - [Ordinary least squares for the general linear model](/P/glm-ols)
 - [Posterior density is proportional to joint likelihood](/P/post-jl)
-- [Probability density function of the Dirichlet distribution](/P/dir-pdf)
-- [Probability density function of the Wald distribution](/P/wald-pdf)
 - [Probability density function of the beta distribution](/P/beta-pdf)
 - [Probability density function of the continuous uniform distribution](/P/cuni-pdf)
+- [Probability density function of the Dirichlet distribution](/P/dir-pdf)
 - [Probability density function of the exponential distribution](/P/exp-pdf)
 - [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 normal distribution](/P/norm-pdf)
+- [Probability density function of the Wald distribution](/P/wald-pdf)
 - [Probability mass function of the Bernoulli distribution](/P/bern-pmf)
-- [Probability mass function of the Poisson distribution](/P/poiss-pmf)
 - [Probability mass function of the binomial distribution](/P/bin-pmf)
 - [Probability mass function of the categorical distribution](/P/cat-pmf)
 - [Probability mass function of the discrete uniform distribution](/P/duni-pmf)
 - [Probability mass function of the multinomial distribution](/P/mult-pmf)
+- [Probability mass function of the Poisson distribution](/P/poiss-pmf)
 - [Quantile function of the continuous uniform distribution](/P/cuni-qf)
 - [Quantile function of the discrete uniform distribution](/P/duni-qf)
 - [Quantile function of the exponential distribution](/P/exp-qf)
-- [Relationship between R² and maximum log-likelihood](/P/rsq-mll)
 - [Relationship between covariance and correlation](/P/cov-corr)
 - [Relationship between gamma distribution and standard gamma distribution](/P/gam-sgam)
 - [Relationship between gamma distribution and standard gamma distribution](/P/gam-sgam2)
@@ -84,6 +83,7 @@ title: "Proofs without Source"
 - [Relationship between normal distribution and standard normal distribution](/P/norm-snorm2)
 - [Relationship between normal distribution and standard normal distribution](/P/norm-snorm3)
 - [Relationship between precision matrix and correlation matrix](/P/precmat-corrmat)
+- [Relationship between R² and maximum log-likelihood](/P/rsq-mll)
 - [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)

update.py

@@ -59,7 +59,7 @@
             if line.find('title:') == 0:
                 title      = re.sub('"', '', line[7:-1])
                 title_edit = re.sub('[^a-zA-Z- ]', '', title)
-                title_sort = title_edit[0].upper() + title_edit[1:]
+                title_sort = title_edit.upper()
             if line.find('author:') == 0:
                 author = re.sub('"', '', line[8:-1])
             if line.find('username:') == 0:
@@ -114,7 +114,7 @@
             if line.find('title:') == 0:
                 title      = re.sub('"', '', line[7:-1])
                 title_edit = re.sub('[^a-zA-Z- ]', '', title)
-                title_sort = title_edit[0].upper() + title_edit[1:]
+                title_sort = title_edit.upper()
             if line.find('author:') == 0:
                 author = re.sub('"', '', line[8:-1])
             if line.find('username:') == 0: