The Book of Statistical Proofs

Proof #525: "Marginal distributions of the multivariate t-distribution" (mvt-marg) #NewProof
statproofbook.github.io/P/mvt-marg

Proof #524: "Second-order expectations for the matrix-normal distribution" (matn-meanso) #NewProof
statproofbook.github.io/P/matn-meanso

Thanks! 👍

Proof #523: "Expectation of quadratic forms for the matrix-normal distribution" (matn-meanqf) #NewProof
statproofbook.github.io/P/matn-meanqf

DOI or URL?

Proof #522: "Cross-covariance matrices of the matrix-normal distribution" (matn-ccm) #NewProof
statproofbook.github.io/P/matn-ccm

Consider this a compliment... 😁

Haha... 😂 Nice to hear it's rigorous! Any ideas to make it less messy? 🤔

Proof #521: "Chi-squared distribution is a special case of gamma distribution" (chi2-gam2) #NewProof
statproofbook.github.io/P/chi2-gam2

Proof #428: "Maximum-a-posteriori estimation for multinomial observations" (mult-map) #RandomProof
statproofbook.github.io/P/mult-map

Proof #24: "Mean of the categorical distribution" (cat-mean) #RandomProof
statproofbook.github.io/P/cat-mean

Proof #309: "Corrected Akaike information criterion for multiple linear regression" (mlr-aicc) #RandomProof
statproofbook.github.io/P/mlr-aicc

Proof #113: "Relation of discrete Kullback-Leibler divergence to Shannon entropy" (kl-ent) #RandomProof
statproofbook.github.io/P/kl-ent

Proof #112: "Relationship between gamma distribution and standard gamma distribution" (gam-sgam) #RandomProof
statproofbook.github.io/P/gam-sgam

Proof #135: "Projection matrix and residual-forming matrix are idempotent" (mlr-idem) #RandomProof
statproofbook.github.io/P/mlr-idem

Proof #261: "Addition of the differential entropy upon multiplication with invertible matrix" (dent-addvec) #RandomProof
statproofbook.github.io/P/dent-addvec

Proof #51: "Mode of the exponential distribution" (exp-mode) #RandomProof
statproofbook.github.io/P/exp-mode

Proof #257: "Probability mass function of a sum of independent discrete random variables" (pmf-sumind) #RandomProof
statproofbook.github.io/P/pmf-sumind

Proof #371: "Ordinary least squares for two-way analysis of variance" (anova2-ols) #RandomProof
statproofbook.github.io/P/anova2-ols

Proof #308: "Bayesian information criterion for multiple linear regression" (mlr-bic) #RandomProof
statproofbook.github.io/P/mlr-bic

Proof #25: "Mean of the multinomial distribution" (mult-mean) #RandomProof
statproofbook.github.io/P/mult-mean

Proof #414: "Equivalence of operations for model evidence and log model evidence" (lme-mean) #RandomProof
statproofbook.github.io/P/lme-mean

Proof #18: "Variance of the normal distribution" (norm-var) #RandomProof
statproofbook.github.io/P/norm-var

Proof #277: "The residuals and the covariate are uncorrelated in simple linear regression" (slr-rescorr) #RandomProof
statproofbook.github.io/P/slr-rescorr

Proof #353: "Symmetry of the covariance" (cov-symm) #RandomProof
statproofbook.github.io/P/cov-symm

Proof #180: "Relationship between normal distribution and standard normal distribution" (norm-snorm3) #RandomProof
statproofbook.github.io/P/norm-snorm3

Proof #118: "Partition of covariance into expected values" (cov-mean) #RandomProof
statproofbook.github.io/P/cov-mean

Proof #347: "Invariance of the covariance matrix under addition of constant vector" (covmat-inv) #RandomProof
statproofbook.github.io/P/covmat-inv

Proof #476: "Mutual information of the bivariate normal distribution" (bvn-mi) #RandomProof
statproofbook.github.io/P/bvn-mi

Proof #324: "Normal-gamma distribution is a special case of normal-Wishart distribution" (ng-nw) #RandomProof
statproofbook.github.io/P/ng-nw