aperr_sf {scoringfunctions} | R Documentation |
Absolute percentage error scoring function
Description
The function aperr_sf computes the absolute percentage error scoring function
when y
materializes and x
is the predictive
\textnormal{med}^{(-1)}(F)
functional.
The absolute percentage error scoring function is defined in Table 1 in Gneiting (2011).
Usage
aperr_sf(x, y)
Arguments
x |
Predictive |
y |
Realization (true value) of process. It can be a vector of length
|
Details
The absolute percentage error scoring function is defined by:
S(x, y) := |(x - y)/y|
Domain of function:
x > 0
y > 0
Range of function:
S(x, y) \geq 0, \forall x, y > 0
Value
Vector of absolute percentage errors.
Note
For details on the absolute percentage error scoring function, see Gneiting (2011).
The \beta
-median functional, \textnormal{med}^{(\beta)}(F)
is the
median of a probability distribution whose density is proportional to
y^\beta f(y)
, where f
is the density of the probability distribution
F
of y
(Gneiting 2011).
The absolute percentage error scoring function is negatively oriented (i.e. the smaller, the better).
The absolute percentage error scoring function is strictly consistent for the
\textnormal{med}^{(-1)}(F)
functional relative to the family
\mathbb{F}
of potential probability distributions (whose densities are
proportional to y^{-1} f(y)
, where f
is the density of the
probability distribution F
for the future y
) for which the first
moment exists and is finite (see Theorems 5 and 9 in Gneiting 2011).
References
Gneiting T (2011) Making and evaluating point forecasts. Journal of the American Statistical Association 106(494):746–762. doi:10.1198/jasa.2011.r10138.
Examples
# Compute the absolute percentage error scoring function.
df <- data.frame(
y = rep(x = 2, times = 3),
x = 1:3
)
df$absolute_percentage_error <- aperr_sf(x = df$x, y = df$y)
print(df)