meanlog_if: Log-transformed identification function

In scoringfunctions: Loss Functions for Assessing Point Forecasts

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)

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

Value

Vector of values of the log-transformed identification function.

Note

The \exp(\textnormal{E}_F[\log(Y)]) functional is the geometric mean of the probability distribution F of Y, i.e. the r = 0 case of the generalized (power) mean of order r defined by eq. (2.1) in Yeh et al. (2008).

The log-transformed identification function is a strict \mathbb{F}-identification function for the log-transformed expectation \exp(\textnormal{E}_F[\log(Y)]) (Tyralis and Papacharalampous 2026).

\mathbb{F} is the family of probability distributions F for which \textnormal{E}_F[\log(Y)] exists and is finite (Tyralis and Papacharalampous 2026).

References

Tyralis H, Papacharalampous G (2026) Variable transformations in consistent loss functions. Knowledge-Based Systems 336:115202. \Sexpr[results=rd]{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. \Sexpr[results=rd]{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)

scoringfunctions documentation built on Aug. 30, 2026, 5:07 p.m.