scoringfunctions (version 1.1)

serrlog_sf: Squared error log scoring function

Description

The function serrlog_sf computes the squared error log scoring function when $y$ materialises and $x$ is the $\exp ({\text{E}}_F[\log (Y)])$ predictive functional.

The squared error log scoring function is defined in Houghton-Carr (1999).

Usage

serrlog_sf(x, y)

Value

Vector of squared errors of log-transformed variables.

Arguments

x

Predictive $\exp ({\text{E}}_F[\log (Y)])$ functional (prediction). It can be a vector of length $n$ (must have the same length as $y$).

y

Realisation (true value) of process. It can be a vector of length $n$ (must have the same length as $x$).

Details

The squared error scoring function is defined by:

$$S(x,y):=(\log (x)-\log (y){)}^2$$

Domain of function:

$$x>0$$

$$y>0$$

Range of function:

$$S(x,y)\ge 0,\mathrm{\forall }x,y>0$$

References

Houghton-Carr HA (1999) Assessment criteria for simple conceptual daily rainfall-runoff models. Hydrological Sciences Journal 44(2):237--261. tools:::Rd_expr_doi("10.1080/02626669909492220").

Tyralis H, Papacharalampous G (2025) Transformations of predictions and realizations in consistent scoring functions. tools:::Rd_expr_doi("10.48550/arXiv.2502.16542").

Examples

# Compute the squarer error log scoring function.

df <- data.frame(
    y = rep(x = 2, times = 3),
    x = 1:3
)

df$squaredlog_error <- serrlog_sf(x = df$x, y = df$y)

print(df)