fitdistcp - Distribution Fitting with Calibrating Priors for Commonly Used Distributions

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>.