scoringfunctions (version 1.2)

meanlog_if: Log-transformed identification function

Description

The function meanlog_if computes the log-transformed identification function, when \(y\) materialises and \(\exp(\textnormal{E}_F[\log(Y)])\), the geometric mean of \(F\) (Yeh et al. 2008), is the predictive functional.

The log-transformed identification function is defined in Tyralis and Papacharalampous (2026).

Usage

meanlog_if(x, y)

Value

Vector of values of the log-transformed identification function.

Arguments

x

Predictive \(\exp(\textnormal{E}_F[\log(Y)])\) functional. 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 log-transformed identification function is defined by:

$$V(x, y) := \log(x) - \log(y)$$

Domain of function:

$$x > 0$$

$$y > 0$$

Range of function:

$$V(x, y) \in \mathbb{R}, \forall x, y > 0$$

References

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_sf, serrlog_rs

Examples

# Compute the log-transformed identification function.

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

df$meanlog_if <- meanlog_if(x = df$x, y = df$y)

print(df)