The Book of Statistical Proofs
@statproofbook.bsky.social
– a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences. #StatProofBook #RandomProof
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How to submit a new theorem to The Book of Statistical Proofs
YouTube video by Joram Soch
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How to submit a new theorem to The Book of Statistical Proofs
www.youtube.com/watch?v=ZMCH...
www.youtube.com/watch?v=ZMCH...
Proof #230: "Variance of the Poisson distribution" (poiss-var) #RandomProof
statproofbook.github.io/P/poiss-var
statproofbook.github.io/P/poiss-var
Variance of the Poisson distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 21, 2025 at 7:31 AM
Proof #230: "Variance of the Poisson distribution" (poiss-var) #RandomProof
statproofbook.github.io/P/poiss-var
statproofbook.github.io/P/poiss-var
Proof #64: "Log Bayes factor in terms of log model evidences" (lbf-lme) #RandomProof
statproofbook.github.io/P/lbf-lme
statproofbook.github.io/P/lbf-lme
Log Bayes factor in terms of log model evidences
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 20, 2025 at 8:35 AM
Proof #64: "Log Bayes factor in terms of log model evidences" (lbf-lme) #RandomProof
statproofbook.github.io/P/lbf-lme
statproofbook.github.io/P/lbf-lme
Proof #422: "Kullback-Leibler divergence for the continuous uniform distribution" (cuni-kl) #RandomProof
statproofbook.github.io/P/cuni-kl
statproofbook.github.io/P/cuni-kl
Kullback-Leibler divergence for the continuous uniform distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 19, 2025 at 9:24 AM
Proof #422: "Kullback-Leibler divergence for the continuous uniform distribution" (cuni-kl) #RandomProof
statproofbook.github.io/P/cuni-kl
statproofbook.github.io/P/cuni-kl
Proof #35: "Marginal distributions of the multivariate normal distribution" (mvn-marg) #RandomProof
statproofbook.github.io/P/mvn-marg
statproofbook.github.io/P/mvn-marg
Marginal distributions of the multivariate normal distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 18, 2025 at 9:03 AM
Proof #35: "Marginal distributions of the multivariate normal distribution" (mvn-marg) #RandomProof
statproofbook.github.io/P/mvn-marg
statproofbook.github.io/P/mvn-marg
Proof #70: "Probability density function of the matrix-normal distribution" (matn-pdf) #RandomProof
statproofbook.github.io/P/matn-pdf
statproofbook.github.io/P/matn-pdf
Probability density function of the matrix-normal distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 17, 2025 at 8:13 AM
Proof #70: "Probability density function of the matrix-normal distribution" (matn-pdf) #RandomProof
statproofbook.github.io/P/matn-pdf
statproofbook.github.io/P/matn-pdf
Proof #197: "Probability density function of the chi-squared distribution" (chi2-pdf) #RandomProof
statproofbook.github.io/P/chi2-pdf
statproofbook.github.io/P/chi2-pdf
Probability density function of the chi-squared distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 16, 2025 at 8:46 AM
Proof #197: "Probability density function of the chi-squared distribution" (chi2-pdf) #RandomProof
statproofbook.github.io/P/chi2-pdf
statproofbook.github.io/P/chi2-pdf
Proof #383: "Log Bayes factor for binomial observations" (bin-lbf) #RandomProof
statproofbook.github.io/P/bin-lbf
statproofbook.github.io/P/bin-lbf
Log Bayes factor for binomial observations
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 15, 2025 at 8:31 AM
Proof #383: "Log Bayes factor for binomial observations" (bin-lbf) #RandomProof
statproofbook.github.io/P/bin-lbf
statproofbook.github.io/P/bin-lbf
Proof #361: "Value of the probability-generating function for argument zero" (pgf-zero) #RandomProof
statproofbook.github.io/P/pgf-zero
statproofbook.github.io/P/pgf-zero
Value of the probability-generating function for argument zero
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 13, 2025 at 3:31 PM
Proof #361: "Value of the probability-generating function for argument zero" (pgf-zero) #RandomProof
statproofbook.github.io/P/pgf-zero
statproofbook.github.io/P/pgf-zero
Proof #39: "Quantile function of the continuous uniform distribution" (cuni-qf) #RandomProof
statproofbook.github.io/P/cuni-qf
statproofbook.github.io/P/cuni-qf
Quantile function of the continuous uniform distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 12, 2025 at 8:30 AM
Proof #39: "Quantile function of the continuous uniform distribution" (cuni-qf) #RandomProof
statproofbook.github.io/P/cuni-qf
statproofbook.github.io/P/cuni-qf
Proof #311: "Mode of the log-normal distribution" (lognorm-mode) #RandomProof
statproofbook.github.io/P/lognorm-mode
statproofbook.github.io/P/lognorm-mode
Mode of the log-normal distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 11, 2025 at 9:22 AM
Proof #311: "Mode of the log-normal distribution" (lognorm-mode) #RandomProof
statproofbook.github.io/P/lognorm-mode
statproofbook.github.io/P/lognorm-mode
Proof #421: "Skewness of the Wald distribution" (wald-skew) #RandomProof
statproofbook.github.io/P/wald-skew
statproofbook.github.io/P/wald-skew
Skewness of the Wald distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 10, 2025 at 7:55 AM
Proof #421: "Skewness of the Wald distribution" (wald-skew) #RandomProof
statproofbook.github.io/P/wald-skew
statproofbook.github.io/P/wald-skew
Proof #254: "Probability density function of an invertible function of a continuous random vector" (pdf-invfct) #RandomProof
statproofbook.github.io/P/pdf-invfct
statproofbook.github.io/P/pdf-invfct
Probability density function of an invertible function of a continuous random vector
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 9, 2025 at 8:33 AM
Proof #254: "Probability density function of an invertible function of a continuous random vector" (pdf-invfct) #RandomProof
statproofbook.github.io/P/pdf-invfct
statproofbook.github.io/P/pdf-invfct
Proof #224: "Maximum likelihood estimation for the Poisson distribution with exposure values" (poissexp-mle) #RandomProof
statproofbook.github.io/P/poissexp-mle
statproofbook.github.io/P/poissexp-mle
Maximum likelihood estimation for the Poisson distribution with exposure values
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 8, 2025 at 1:30 PM
Proof #224: "Maximum likelihood estimation for the Poisson distribution with exposure values" (poissexp-mle) #RandomProof
statproofbook.github.io/P/poissexp-mle
statproofbook.github.io/P/poissexp-mle
Proof #281: "Simple linear regression is a special case of multiple linear regression" (slr-mlr) #RandomProof
statproofbook.github.io/P/slr-mlr
statproofbook.github.io/P/slr-mlr
Simple linear regression is a special case of multiple linear regression
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 7, 2025 at 2:08 PM
Proof #281: "Simple linear regression is a special case of multiple linear regression" (slr-mlr) #RandomProof
statproofbook.github.io/P/slr-mlr
statproofbook.github.io/P/slr-mlr
Proof #250: "Normal distribution maximizes differential entropy for fixed variance" (norm-maxent) #RandomProof
statproofbook.github.io/P/norm-maxent
statproofbook.github.io/P/norm-maxent
Normal distribution maximizes differential entropy for fixed variance
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 6, 2025 at 9:17 AM
Proof #250: "Normal distribution maximizes differential entropy for fixed variance" (norm-maxent) #RandomProof
statproofbook.github.io/P/norm-maxent
statproofbook.github.io/P/norm-maxent
Proof #393: "Independence of estimated parameters and residuals in multiple linear regression" (mlr-ind) #RandomProof
statproofbook.github.io/P/mlr-ind
statproofbook.github.io/P/mlr-ind
Independence of estimated parameters and residuals in multiple linear regression
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 4, 2025 at 8:22 AM
Proof #393: "Independence of estimated parameters and residuals in multiple linear regression" (mlr-ind) #RandomProof
statproofbook.github.io/P/mlr-ind
statproofbook.github.io/P/mlr-ind
Proof #458: "Equivalence of log-likelihood ratio and mutual information for the general linear model" (glm-llrmi) #RandomProof
statproofbook.github.io/P/glm-llrmi
statproofbook.github.io/P/glm-llrmi
Equivalence of log-likelihood ratio and mutual information for the general linear model
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 3, 2025 at 8:11 AM
Proof #458: "Equivalence of log-likelihood ratio and mutual information for the general linear model" (glm-llrmi) #RandomProof
statproofbook.github.io/P/glm-llrmi
statproofbook.github.io/P/glm-llrmi
Proof #267: "Distribution of the inverse general linear model" (iglm-dist) #RandomProof
statproofbook.github.io/P/iglm-dist
statproofbook.github.io/P/iglm-dist
Distribution of the inverse general linear model
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 2, 2025 at 8:52 AM
Proof #267: "Distribution of the inverse general linear model" (iglm-dist) #RandomProof
statproofbook.github.io/P/iglm-dist
statproofbook.github.io/P/iglm-dist
Proof #465: "Monotonicity of probability" (prob-mon2) #RandomProof
statproofbook.github.io/P/prob-mon2
statproofbook.github.io/P/prob-mon2
Monotonicity of probability
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
November 1, 2025 at 8:27 AM
Proof #465: "Monotonicity of probability" (prob-mon2) #RandomProof
statproofbook.github.io/P/prob-mon2
statproofbook.github.io/P/prob-mon2
Proof #52: "Non-negativity of the expected value" (mean-nonneg) #RandomProof
statproofbook.github.io/P/mean-nonneg
statproofbook.github.io/P/mean-nonneg
Non-negativity of the expected value
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
October 31, 2025 at 8:38 AM
Proof #52: "Non-negativity of the expected value" (mean-nonneg) #RandomProof
statproofbook.github.io/P/mean-nonneg
statproofbook.github.io/P/mean-nonneg
Proof #520: "Mode of the beta distribution" (beta-mode) #NewProof
statproofbook.github.io/P/beta-mode
statproofbook.github.io/P/beta-mode
Mode of the beta distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
October 30, 2025 at 9:26 AM
Proof #520: "Mode of the beta distribution" (beta-mode) #NewProof
statproofbook.github.io/P/beta-mode
statproofbook.github.io/P/beta-mode
Proof #178: "Cumulative distribution function of the gamma distribution" (gam-cdf) #RandomProof
statproofbook.github.io/P/gam-cdf
statproofbook.github.io/P/gam-cdf
Cumulative distribution function of the gamma distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
October 30, 2025 at 9:25 AM
Proof #178: "Cumulative distribution function of the gamma distribution" (gam-cdf) #RandomProof
statproofbook.github.io/P/gam-cdf
statproofbook.github.io/P/gam-cdf
Proof #519: "Median of the beta distribution" (beta-med) #NewProof
statproofbook.github.io/P/beta-med
statproofbook.github.io/P/beta-med
Median of the beta distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
October 29, 2025 at 10:59 AM
Proof #519: "Median of the beta distribution" (beta-med) #NewProof
statproofbook.github.io/P/beta-med
statproofbook.github.io/P/beta-med
Proof #95: "Probability density function of the Dirichlet distribution" (dir-pdf) #RandomProof
statproofbook.github.io/P/dir-pdf
statproofbook.github.io/P/dir-pdf
Probability density function of the Dirichlet distribution
The Book of Statistical Proofs – a centralized, open and collaboratively edited archive of statistical theorems for the computational sciences
statproofbook.github.io
October 29, 2025 at 8:27 AM
Proof #95: "Probability density function of the Dirichlet distribution" (dir-pdf) #RandomProof
statproofbook.github.io/P/dir-pdf
statproofbook.github.io/P/dir-pdf