dispersion: Dispersion based on the Variance of the Probability Integral...

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

Dispersion based on the Variance of the Probability Integral Transform

Description

This function calculates dispersion based on the variance of the Probability Integral Transform (Var(PIT)).

Usage

dispersion(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 variance is calculated in terms of the sample variance of the PIT values.

The variance of the PIT values (Var(PIT)) provides information on the dispersion of a calibrated predictive distribution. A variance of the PIT values equal to 1/12 ≈ 0.0833 corresponds to the variance of the uniform distribution on [0,1], which is desirable. A variance greater than 1/12 indicates underdispersion and a variance smaller than 1/12 indicates overdispersion of the predictive distribution.

Value

Variance in terms of the sample variance 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.

Examples

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

# dispersion calculation via Var(PIT)
dispersion(u = u)

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