meanlog_if {scoringfunctions} | R Documentation |
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)])
is the
predictive functional.
The log-transformed identification function is defined in Tyralis and Papacharalampous (2025).
Usage
meanlog_if(x, y)
Arguments
x |
Predictive |
y |
Realisation (true value) of process. It can be a vector of length
|
Details
The mean 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 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 2025).
\mathbb{F}
is the family of probability distributions F
for which
\textnormal{E}_F[\log(Y)]
exists and is finite (Tyralis and
Papacharalampous 2025).
References
Tyralis H, Papacharalampous G (2025) Transformations of predictions and realizations in consistent scoring functions. doi:10.48550/arXiv.2502.16542.
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)