linex_rs: Realised LINEX score

In scoringfunctions: Loss Functions for Assessing Point Forecasts

Realised LINEX score

Description

The function linex_rs computes the realised LINEX score with parameter a, when \textbf{\textit{y}} materialises and \textbf{\textit{x}} is the prediction.

Realised LINEX score is a realised score corresponding to the LINEX scoring function linex_sf.

Usage

linex_rs(x, y, a)

Arguments

x	Prediction. It can be a vector of length n (must have the same length as \textbf{\textit{y}}).
y	Realisation (true value) of process. It can be a vector of length n (must have the same length as \textbf{\textit{x}}).
a	It can be a scalar.

Details

The realised LINEX score is defined by:

S(\textbf{\textit{x}}, \textbf{\textit{y}}, a) := (1/n) \sum_{i = 1}^{n} L(x_i, y_i, a)

where

\textbf{\textit{x}} = (x_1, ..., x_n)^\mathsf{T}

\textbf{\textit{y}} = (y_1, ..., y_n)^\mathsf{T}

and

L(x, y, a) := \textnormal{e}^{a (x - y)} - a (x - y) - 1

Domain of function:

\textbf{\textit{x}} \in \mathbb{R}^n

\textbf{\textit{y}} \in \mathbb{R}^n

a \neq 0

Range of function:

S(\textbf{\textit{x}}, \textbf{\textit{y}}, a) \geq 0, \forall \textbf{\textit{x}}, \textbf{\textit{y}} \in \mathbb{R}^n, a \neq 0

Value

Value of the realised LINEX score.

Note

For details on the LINEX scoring function, see linex_sf.

The concept of realised (average) scores is defined by Gneiting (2011) and Fissler and Ziegel (2019).

The realised LINEX score is the realised (average) score corresponding to the LINEX scoring function.

References

Fissler T, Ziegel JF (2019) Order-sensitivity and equivariance of scoring functions. Electronic Journal of Statistics 13(1):1166–1211. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1214/19-EJS1552")}.

Gneiting T (2011) Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746–762. \Sexpr[results=rd]{tools:::Rd_expr_doi("10.1198/jasa.2011.r10138")}.

See Also

linex_sf

Examples

# Compute the realised LINEX score.

set.seed(12345)

a <- 1

x <- 0

y <- rnorm(n = 100, mean = 0, sd = 1)

print(linex_rs(x = x, y = y, a = a))

print(linex_rs(x = rep(x = x, times = 100), y = y, a = a))

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