scoringfunctions (version 1.2)

meanexp_if: Exp-transformed identification function

Description

The function meanexp_if computes the exp-transformed identification function with parameter \(a\), when \(y\) materialises and \((1/a) \log(\textnormal{E}_F[\exp(aY)])\) is the predictive functional.

The exp-transformed identification function is defined by Remark 1 in Tyralis and Papacharalampous (2026), applied to \(g(t) = \exp(at)\).

Usage

meanexp_if(x, y, a)

Value

Vector of values of the exp-transformed identification function.

Arguments

x

Predictive \((1/a) \log(\textnormal{E}_F[\exp(aY)])\) 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 \(x\)).

a

It can be a vector of length \(n\) (must have the same length as \(y\)).

Details

The exp-transformed identification function is defined by:

$$V(x, y, a) := \exp(a x) - \exp(a y)$$

Domain of function:

$$x \in \mathbb{R}$$

$$y \in \mathbb{R}$$

$$a \neq 0$$

Range of function:

$$V(x, y, a) \in \mathbb{R}$$

References

Gerber HU (1974) On additive premium calculation principles. ASTIN Bulletin: The Journal of the IAA 7(3):215--222. tools:::Rd_expr_doi("10.1017/S0515036100006061").

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").

See Also

serrexp_sf, serrexp_rs

Examples

# Compute the exp-transformed identification function.

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

df$meanexp_if <- meanexp_if(x = df$x, y = df$y, a = df$a)

print(df)