pit: Probability integral transform (PIT)

Description

Computes the probability integral transform (PIT) of IDR or raw forecasts.

Usage

pit(predictions, y, randomize = TRUE, seed = NULL)
# S3 method for idr
pit(predictions, y, randomize = TRUE, seed = NULL)
# S3 method for data.frame
pit(predictions, y, randomize = TRUE, seed = NULL)

Arguments

predictions

either an object of class idr (output of predict.idrfit), or a data.frame of numeric variables. In the latter case, the PIT is computed using the empirical distribution of the variables in predictions.

a numeric vector of obervations of the same length as the number of predictions.

randomize

PIT values should be randomized at discontinuity points of the predictive CDF (e.g. at zero for precipitation forecasts). Set randomize = TRUE to randomize.

seed

argument to set.seed for random number generation (if randomize is TRUE).

Value

Vector of PIT values.

References

Gneiting, T., Balabdaoui, F. and Raftery, A. E. (2007), 'Probabilistic forecasts, calibration and sharpness', Journal of the Royal Statistical Society: Series B (Statistical Methodology) 69(2), 243-268.

Examples

Run this code

# NOT RUN {
data("rain")
require("graphics")

## Postprocess HRES forecast using data of 4 years

X <- rain[1:(4 * 365), "HRES", drop = FALSE]
y <- rain[1:(4 * 365), "obs"]

fit <- idr(y = y, X = X)

## Assess calibration of the postprocessed HRES forecast using data of next 4
## years and compare to calibration of the raw ensemble

data <- rain[(4 * 365 + 1):(8 * 365), "HRES", drop = FALSE]
obs <- rain[(4 * 365 + 1):(8 * 365), "obs"]
predictions <- predict(fit, data = data)
idrPit <- pit(predictions, obs, seed = 123)

rawData <- rain[(4 * 365 + 1):(8 * 365), c("HRES", "CTR", paste0("P", 1:50))]
rawPit <- pit(rawData, obs, seed = 123)

hist(idrPit, xlab = "Probability Integral Transform",
  ylab = "Density", freq = FALSE, main = "Postprocessed HRES")
hist(rawPit, xlab = "Probability Integral Transform",
  ylab = "Density", freq = FALSE, main = "Raw ensemble")
# }