Distribution Fitting with Calibrating Priors for Commonly Used Distributions
Generates a comment about the method
Generates a comment about the method
Evaluate DMGS equation 3.3
determine revert2ml or not
Cauchy Distribution Predictions Based on a Calibrating Prior
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
Cauchy Distribution with a Predictor, Predictions Based on a Calibrati...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
Cauchy-with-p1 observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
Cauchy distribution: RHP mean
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 2.1, p1 term
DMGS equation 2.1, p2 term
Predicted Parameter and Generalized Residuals
Waic
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
Waic
Generates a comment about the method
Cauchy-with-p1 density function
Densities from MLE and RHP
Densities from MLE and RHP
Extract the results from derivatives and put them into f2
Extract the results from derivatives and put them into ldd
Extract the results from derivatives and put them into ldd
Extract the results from derivatives and put them into lddd
Exponential-with-p1 density function
Densities from MLE and RHP
Densities from MLE and RHP
Frechet_k1-with-p2 density function
Densities from MLE and RHP
Densities from MLE and RHP
Densities from MLE and RHP
Densities from MLE and RHP
GEVD-with-p1: Density function
GEVD-with-p1: Density function
GEVD-with-p1: Density function
Densities for 5 predictions
Densities for 5 predictions
GEV-with-known-shape-with-p1 density function
Densities from MLE and RHP
Densities for 5 predictions
Densities for 5 predictions
Densities from MLE and RHP
Densities for 5 predictions
Gumbel-with-p1 density function
Densities from MLE and RHP
Densities from MLE and RHP
Densities from MLE and RHP
Densities from MLE and cp
Densities from MLE and RHP
Densities from MLE and RHP
Normal-with-p1 density function
Densities from MLE and RHP
Densities from MLE and RHP
Logistic-with-p1 density function
Densities from MLE and RHP
Densities from MLE and RHP
Densities from MLE and RHP
LST-with-p1 density function
Densities from MLE and RHP
Evaluate DMGS equation 3.3
Densities from MLE and RHP
Linear regression formula, densities
Normal-with-p1 density function
Densities from MLE and RHP
Densities from MLE and RHP
Densities from MLE and RHP
pareto_k1-with-p2 density function
Densities from MLE and RHP
Predictive PDFs
Weibull-with-p1 density function
Densities from MLE and RHP
Densities from MLE and RHP
Exponential Distribution Predictions Based on a Calibrating Prior
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Third derivative of the normalized log-likelihood
The second derivative of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the log-likelihood
The third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
Log scores for MLE and RHP predictions calculated using leave-one-out
Exponential Distribution with a Predictor, Predictions Based on a Cali...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
exp distribution: RHP means
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 2.1, p1 term
The first derivative of the cdf
DMGS equation 2.1, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Waic
The first derivative of the cdf
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Waicscores
Deal with situations in which the user wants d or p outside the GEV ra...
Deal with situations in which the user wants d or p outside the GPD ra...
Frechet Distribution Predictions Based on a Calibrating Prior
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 3.3, p1 term
The first derivative of the cdf
DMGS equation 3.3, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Waic
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
MLE and RHP predictive means
Frechet Distribution with Predictor, Predictions Based on a Calibratin...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
frechet_k1 distribution: RHP mean
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 2.1, p1 term
The first derivative of the cdf
DMGS equation 2.1, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Waic
Gamma Distribution Predictions Based on a Calibrating Prior
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the expected log-likelihood
One component of the second derivative of the expected log-likelihood
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
MLE and RHP predictive means
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
Waic
Check MLE
Generalized Extreme Value Distribution, Predictions Based on a Calibra...
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Derivative of expected information matrix, based on MEV routine gev.in...
Derivative of inverse expected information matrix, based on MEV routin...
Temporary dummy for one of the ppm models
Generalized Extreme Value Distribution with Known Shape, Predictions B...
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
MLE and RHP means
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Waic
The combined derivative of the normalized log-likelihood
The first derivative of the normalized log-likelihood
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
First derivative of the log density Created by Stephen Jewson using De...
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Analytical Expressions for Predictive Means RHP mean based on the expe...
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
Check MLE
Generalized Extreme Value Distribution with a Predictor, Predictions B...
DMGS equation 2.1, f1 term
The first derivative of the density
GEVD-with-p1: DMGS equation 1.2 f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Derivative of information matrix, based on ldd
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood, with fixed s...
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
observed log-likelihood function
Analytical expressions for Predictive Means RHP mean based on the expe...
GEVD-with-p1: DMGS equation 3.3 mu1 term
Minus the first derivative of the cdf, at alpha
GEVD-with-p1: DMGS equation 3.3 mu2 term
Minus the second derivative of the cdf, at alpha
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Set initial conditions
Waic
Check MLE
Generalized Extreme Value Distribution with Two Predictors, Prediction...
DMGS equation 2.1, f1 term
The first derivative of the density
GEVD-with-p1: DMGS equation 1.2 f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Derivative of information matrix, based on ldd
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood, with fixed s...
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
observed log-likelihood function
Analytical expressions for Predictive Means RHP mean based on the expe...
GEVD-with-p1: DMGS equation 3.3 mu1 term
Minus the first derivative of the cdf, at alpha
GEVD-with-p1: DMGS equation 3.3 mu2 term
Minus the second derivative of the cdf, at alpha
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Set initial conditions
Waic
Check MLE
Generalized Extreme Value Distribution with Three Predictors, Predicti...
DMGS equation 2.1, f1 term, fixed shape parameter DMGS equation 2.1, f...
The first derivative of the density
GEVD-with-p1: DMGS equation 1.2 f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood, with fixed s...
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
observed log-likelihood function
Analytical expressions for Predictive Means RHP mean based on the expe...
GEVD-with-p1: DMGS equation 3.3 mu1 term
Minus the first derivative of the cdf, at alpha
GEVD-with-p1: DMGS equation 3.3 mu2 term
Minus the second derivative of the cdf, at alpha
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Set initial conditions
Waic
DMGS equation 2.1, f1 term, fixed shape parameter
The first derivative of the density
GEVD-with-p1: DMGS equation 1.2 f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood, with fixed ...
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood, with fixed s...
The third derivative of the normalized log-likelihood
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
GEVD-with-p1: DMGS equation 3.3 mu1 term, fixed shape parameter
Minus the first derivative of the cdf, at alpha
GEVD-with-p1: DMGS equation 3.3 mu2 term, fixed shape parameter
Minus the second derivative of the cdf, at alpha
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
GEV Distribution with Known Shape with a Predictor, Predictions Based ...
DMGS equation 2.1, f1 term, fixed shape parameter
The first derivative of the density
GEVD-with-p1: DMGS equation 1.2 f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood, with fixed ...
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood, with fixed s...
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
GEV-with-known-shape-with-p1 observed log-likelihood function
Analytical expressions for Predictive Means RHP mean based on the expe...
GEVD-with-p1: DMGS equation 3.3 mu1 term, fixed shape parameter
Minus the first derivative of the cdf, at alpha
GEVD-with-p1: DMGS equation 3.3 mu2 term, fixed shape parameter
Minus the second derivative of the cdf, at alpha
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Waic
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
PWM parameter estimation
Set initial conditions
Waic
Generalized Normal Distribution Predictions Based on a Calibrating Pri...
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
One component of the second derivative of the normalized log-likelihoo...
Waic for RUST
Check MLE
Generalized Pareto Distribution with Known Location Parameter, Predict...
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Derivative of expected information matrix, based on MEV routine gpd.in...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Analytical Expressions for Predictive Means RHP mean based on the expe...
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Set initial conditions
Waic
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
One component of the second derivative of the normalized log-likelihoo...
One component of the third derivative of the normalized log-likelihood
Second derivative matrix of the normalized log-likelihood, with fixed ...
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Gumbel Distribution Predictions Based on a Calibrating Prior
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
MLE and RHP predictive means
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
Gumbel Distribution with a Predictor, Predictions Based on a Calibrati...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
Gumbel distribution: RHP mean
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 2.1, p1 term
The first derivative of the cdf
DMGS equation 2.1, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Waic
DMGS equation 3.3, p1 term
The first derivative of the cdf
DMGS equation 3.3, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Waic
Half-Normal Distribution Predictions Based on a Calibrating Prior
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Expected information matrix
Second derivative of the expected log-likelihood
Third derivative of the normalized log-likelihood
The second derivative of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the log-likelihood
The third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
Log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
MLE and RHP predictive means RHP mean based on the expectation of DMGS...
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 2.1, p1 term
DMGS equation 2.1, p2 term
Waic
Inverse Gamma Distribution, Predictions Based on a Calibrating Prior
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Log scores for MLE and cp predictions calculated using leave-one-out
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
Waic
Inverse Gauss Distribution, Predictions Based on a Calibrating Prior
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
MLE and RHP predictive means
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
Waic
Jeffreys' Prior with two parameters
Jeffreys' Prior with three parameters
Jeffreys' Prior with four parameters
Log-normal Distribution Predictions Based on a Calibrating Prior
Log-normal Distribution Predictions Based on a Calibrating Prior, usin...
One component of the second derivative of the expected log-likelihood
One component of the second derivative of the expected log-likelihood
One component of the second derivative of the expected log-likelihood
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
MLE and RHP predictive means
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
Waic
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the lnormalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the lnormalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
Log scores for MLE and RHP predictions calculated using leave-one-out
Minus the first derivative of the cdf, at alpha
Minus the second derivative of the cdf, at alpha
Log-normal Distribution with a Predictor, Predictions Based on a Calib...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
Log-normal-with-p1 observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
Minus the first derivative of the cdf, at alpha
Minus the second derivative of the cdf, at alpha
The first derivative of the cdf
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Waic
The first derivative of the cdf
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Waic for RUST
Logistic Distribution Predictions Based on a Calibrating Prior
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
Logistic Distribution with a Predictor, Predictions Based on a Calibra...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
Logistic-with-p1 observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
Logistic distribution: RHP mean
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 2.1, p1 term
The first derivative of the cdf
DMGS equation 2.1, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Waic
DMGS equation 3.3, p1 term
The first derivative of the cdf
DMGS equation 3.3, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Waic
t Distribution Predictions Based on a Calibrating Prior
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
Waic
t Distribution with a Predictor, Predictions Based on a Calibrating Pr...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
LST-with-p1 observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 2.1, p1 term
DMGS equation 2.1, p2 term
Predicted Parameter and Generalized Residuals
Set initial conditions
Waic
Make WAIC
Calculate MAIC
Make Standard Errors from lddi
Make WAIC
Make muhat0
Calculates quantiles from simulations by inverting the Hazen CDF
Determine t0
Make ta0
A blank function I use for setting up the man page information
Return message for f1f, p1f, mu1f
Return message for f2f, p2f, mu2f
Return message for dsub
Blank function I use for setting up the man page information for the f...
Return message for ldd
Return message for lddd
Return message for lnn
Return message for lnnn
Return message for Logf
Return message for loglik
Return message for logscores
Return message for means
Return message for predictor.
Return message for vector
Return message for WAIC
Move xi away from zero a bit
Illustration of Model Selection Among 10 One Tail Distributions from t...
Illustration of Model Selection Among 18 Distributions from the `fitdi...
Model Selection Among 5 Distributions with predictors from the `fitdis...
Model Selection Among 6 Distributions with predictors from the `fitdis...
Message to explain why GEV and GPD d*** and p*** routines don't re...
Normal Distribution Predictions Based on a Calibrating Prior
Normal Distribution Predictions Based on a Calibrating Prior, using DM...
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
MLE and RHP predictive means
DMGS equation 3.3, mu1 term
DMGS equation 3.3, mu2 term
DMGS equation 3.3, p1 term
DMGS equation 3.3, p2 term
Waic
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the expected per-observation log-likelihoo...
One component of the second derivative of the expected log-likelihood
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
Log scores for MLE and RHP predictions calculated using leave-one-out
Maximum likelihood estimator
Minus the first derivative of the cdf, at alpha
Minus the second derivative of the cdf, at alpha
Normal Distribution with a Predictor, Predictions Based on a Calibrati...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
Normal-with-p1 observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
Maximum likelihood estimator
Minus the first derivative of the cdf, at alpha
Minus the second derivative of the cdf, at alpha
The first derivative of the cdf
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Waic
The first derivative of the cdf
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Method of moments estimator
Waic
Pareto Distribution Predictions Based on a Calibrating Prior
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Third derivative of the normalized log-likelihood
The second derivative of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the log-likelihood
The third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
Log scores for MLE and RHP predictions calculated using leave-one-out
Maximum likelihood estimator
Minus the first derivative of the cdf, at alpha
Minus the second derivative of the cdf, at alpha
The first derivative of the cdf
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Waic
Pareto Distribution with a Predictor, Predictions Based on a Calibrati...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
pareto_k1 distribution: RHP mean
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 2.1, p1 term
The first derivative of the cdf
DMGS equation 2.1, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Waic
Cauchy-with-p1 distribution function
Exponential-with-p1 distribution function
Frechet_k1-with-p2 distribution function
GEVD-with-p1: Distribution function
GEVD-with-p1: Distribution function
GEVD-with-p1: Distribution function
GEV-with-known-shape-with-p1 distribution function
Gumbel-with-p1 distribution function
Normal-with-p1 distribution function
Logistic-with-p1 distribution function
LST-with-p1 distribution function
Linear regression formula, densities
Normal-with-p1 distribution function
pareto_k1-with-p2 distribution function
Predictive CDFs
Weibull-with-p1 distribution function
Cauchy-with-p1 quantile function
-with-p1 quantile function
Frechet_k1-with-p2 quantile function
Temporary dummy for one of the cp models
Temporary dummy for one of the ppm models
Temporary dummy for one of the ppm models
Temporary dummy for one of the ppm models
Temporary dummy for one of the ppm models
GEVD-with-p1: Quantile function
GEVD-with-p1: Quantile function
GEVD-with-p1: Quantile function
GEV-with-known-shape-with-p1 quantile function
Temporary dummy for one of the ppm models
Temporary dummy for one of the ppm models
Gumbel-with-p1 quantile function
Normal-with-p1 quantile function
Logistic-with-p1 quantile function
LST-with-p1 quantile function
Linear regression formula, quantiles
Normal-with-p1 quantile function
Temporary dummy for one of the ppm models
pareto_k1-with-p2 quantile function
Predictive Quantiles
Weibull-with-p1 quantile function
Calculate EP from one model
Calculate MaxEP from one model
Make prediction from one model
Random training data from one model
Evaluation of Reliability for Models in the fitdistcp Package
Cases
Cases
Plotting routine for reltest2
Make prediction from one model
Random training data from one model
Evaluation of Reliability for Certain Additional Models in the `fitdis...
rgev but with maxlik xi guaranteed within bounds
rgev for gev_p1 but with maxlik xi within bounds
rgev for gev_p12 but with maxlik xi within bounds
rgev for gev_p123 but with maxlik xi within bounds
rgpd for gpd_k1 but with maxlik xi within bounds
Generates a comment about the method
Generates a comment about the method
Plotting routine for testppm
Uniform Distribution Predictions Based on a Calibrating Prior
Weibull Distribution Predictions Based on a Calibrating Prior
DMGS equation 3.3, f1 term
The first derivative of the density
DMGS equation 3.3, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the third derivative of the normalized log-likelihood
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
MLE and RHP predictive means
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 3.3, p1 term
The first derivative of the cdf
weibull Distribution with a Predictor on the Scale Parameter, Predicti...
DMGS equation 2.1, f1 term
The first derivative of the density
DMGS equation 2.1, f2 term
The second derivative of the density
First derivative of the density Created by Stephen Jewson using Deriv(...
Second derivative of the density Created by Stephen Jewson using Deriv...
Second derivative matrix of the normalized log-likelihood
The second derivative of the normalized log-likelihood
Third derivative tensor of the normalized log-likelihood
The third derivative of the normalized log-likelihood
One component of the second derivative of the normalized log-likelihoo...
One component of the second derivative of the normalized log-likelihoo...
Logf for RUST
Second derivative of the log density Created by Stephen Jewson using D...
Third derivative of the log density Created by Stephen Jewson using De...
observed log-likelihood function
Log scores for MLE and RHP predictions calculated using leave-one-out
weibull distribution: RHP mean
DMGS equation 3.3, mu1 term
Minus the first derivative of the cdf, at alpha
DMGS equation 3.3, mu2 term
Minus the second derivative of the cdf, at alpha
DMGS equation 2.1, p1 term
The first derivative of the cdf
DMGS equation 2.1, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Predicted Parameter and Generalized Residuals
Waic
DMGS equation 3.3, p2 term
The second derivative of the cdf
First derivative of the cdf Created by Stephen Jewson using Deriv() by...
Second derivative of the cdf Created by Stephen Jewson using Deriv() b...
Waic for RUST
Generates predictive distributions based on calibrating priors for various commonly used statistical models, including models with predictors. Routines for densities, probabilities, quantiles, random deviates and the parameter posterior are provided. The predictions are generated from the Bayesian prediction integral, with priors chosen to give good reliability (also known as calibration). For homogeneous models, the prior is set to the right Haar prior, giving predictions which are exactly reliable. As a result, in repeated testing, the frequencies of out-of-sample outcomes and the probabilities from the predictions agree. For other models, the prior is chosen to give good reliability. Where possible, the Bayesian prediction integral is solved exactly. Where exact solutions are not possible, the Bayesian prediction integral is solved using the Datta-Mukerjee-Ghosh-Sweeting (DMGS) asymptotic expansion. Optionally, the prediction integral can also be solved using posterior samples generated using Paul Northrop's ratio of uniforms sampling package ('rust'). Results are also generated based on maximum likelihood, for comparison purposes. Various model selection diagnostics and testing routines are included. Based on "Reducing reliability bias in assessments of extreme weather risk using calibrating priors", Jewson, S., Sweeting, T. and Jewson, L. (2024); <doi:10.5194/ascmo-11-1-2025>.