bias: Bias based on the Expectation of the Probability Integral...

In jobstdavid/eppverification: Verification Tools for the Statistical Postprocessing of Ensemble Forecasts

Bias based on the Expectation of the Probability Integral Transform

Description

This function calculates bias based on the expectation of the Probability Integral Transform (E(PIT)).

Usage

bias(u, na.action = na.omit)

Arguments

u	vector of PIT values in [0,1] (see details)
na.action	function to handle the NA's. Default: na.omit.

Details

The vector u contains the PIT values u=F(x) for a predictive distribution F and argument x. The expectation is calculated in terms of the sample mean of the PIT values.

The expectation of the PIT values (E(PIT)) provides information on the bias of a calibrated predictive distribution. An expectation of the PIT values equal to 1/2 corresponds to the expectation of the uniform distribution on [0,1], which is desirable. Any deviation from 1/2 indicates that the predictive distribution is biased.

Value

Expectation in terms of the sample mean of the PIT values.

Author(s)

David Jobst

References

Gneiting, T. and Ranjan, R. (2013). Combining predictive distributions. Electronic Journal of Statistics, 7, 1747-1782.

Taillardat, M. et al. (2016). Calibrated Ensemble Forecasts Using Quantile Regression Forests and Ensemble Model Output Statistics. Monthly Weather Review, 144(6), 2375-2393.

Examples

# simulated data
n <- 10000
u <- runif(n)

# bias calculation
bias(u = u)

jobstdavid/eppverification documentation built on May 13, 2024, 5:20 p.m.