scoringfunctions (version 1.2)

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 \(\exp(\textnormal{E}_F[\log(Y)])\) predictive functional, i.e. the geometric mean of \(F\) (Yeh et al. 2008).

The squared error log scoring function is described by eq. (2) in Houghton-Carr (1999).

Usage

serrlog_sf(x, y)

Value

Vector of squared errors of log-transformed variables.

Arguments

x

Predictive \(\exp(\textnormal{E}_F[\log(Y)])\) 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 log scoring function is defined by:

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

Domain of function:

$$x > 0$$

$$y > 0$$

Range of function:

$$S(x, y) \geq 0, \forall x, y > 0$$

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 (2026) Variable transformations in consistent loss functions. Knowledge-Based Systems 336:115202. tools:::Rd_expr_doi("10.1016/j.knosys.2025.115202").

Yeh C-C, Yeh H-W, Chan W (2008) Some equivalent forms of the arithematic-geometric mean inequality in probability: A survey. Journal of Inequalities and Applications 2008:386715. tools:::Rd_expr_doi("10.1155/2008/386715").

See Also

serrlog_rs, meanlog_if

Examples

# Compute the squared 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)