gumbel_p1_mu2f

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>.

Stephen Jewson

fitdistcp

Distribution Fitting with Calibrating Priors for Commonly Used
Distributions

gumbel_p1_mu2f function

<dl><dt>alpha</dt>
<dd>a vector of values of alpha (one minus probability)</dd>
<dt>t0</dt>
<dd>a single value of the predictor (specify either <code>t0</code> or <code>n0</code> but not both)</dd>
<dt>v1</dt>
<dd>first parameter</dd>
<dt>d1</dt>
<dd>the delta used in the numerical derivatives with respect to the parameter</dd>
<dt>v2</dt>
<dd>second parameter</dd>
<dt>d2</dt>
<dd>the delta used in the numerical derivatives with respect to the parameter</dd>
<dt>v3</dt>
<dd>third parameter</dd>
<dt>fd3</dt>
<dd>the fractional delta used in the numerical derivatives with respect to the parameter</dd></dl>

Arguments

DMGS equation 3.3, mu2 term — gumbel_p1_mu2f

<dl>

<dt>alpha</dt>
<dd>a vector of values of alpha (one minus probability)</dd>


<dt>t0</dt>
<dd>a single value of the predictor (specify either <code>t0</code> or <code>n0</code> but not both)</dd>


<dt>v1</dt>
<dd>first parameter</dd>


<dt>d1</dt>
<dd>the delta used in the numerical derivatives with respect to the parameter</dd>


<dt>v2</dt>
<dd>second parameter</dd>


<dt>d2</dt>
<dd>the delta used in the numerical derivatives with respect to the parameter</dd>


<dt>v3</dt>
<dd>third parameter</dd>


<dt>fd3</dt>
<dd>the fractional delta used in the numerical derivatives with respect to the parameter</dd>

</dl>

gumbel_p1_mu2f: DMGS equation 3.3, mu2 term

Description

Usage

Value

Arguments