mape {scoringfunctions} | R Documentation |
Mean absolute percentage error (MAPE)
Description
The function mape computes the mean absolute percentage error when
\textbf{\textit{y}}
materialises and \textbf{\textit{x}}
is the
prediction.
Mean absolute percentage error is a realised score corresponding to the absolute percentage error scoring function aperr_sf.
Usage
mape(x, y)
Arguments
x |
Prediction. It can be a vector of length |
y |
Realisation (true value) of process. It can be a vector of length
|
Details
The mean absolute pecentage error is defined by:
S(\textbf{\textit{x}}, \textbf{\textit{y}}) := (1/n)
\sum_{i = 1}^{n} L(x_i, y_i)
where
\textbf{\textit{x}} = (x_1, ..., x_n)^\mathsf{T}
\textbf{\textit{y}} = (y_1, ..., y_n)^\mathsf{T}
and
L(x, y) := |(x - y)/y|
Domain of function:
\textbf{\textit{x}} > \textbf{0}
\textbf{\textit{y}} > \textbf{0}
where
\textbf{0} = (0, ..., 0)^\mathsf{T}
is the zero vector of length n
and the symbol >
indicates pairwise
inequality.
Range of function:
S(\textbf{\textit{x}}, \textbf{\textit{y}}) \geq 0,
\forall \textbf{\textit{x}}, \textbf{\textit{y}} > \textbf{0}
Value
Value of the mean absolute percentage error.
Note
For details on the absolute percentage error scoring function, see aperr_sf.
The concept of realised (average) scores is defined by Gneiting (2011) and Fissler and Ziegel (2019).
The mean absolute percentage error is the realised (average) score corresponding to the absolute percentage error scoring function.
References
Fissler T, Ziegel JF (2019) Order-sensitivity and equivariance of scoring functions. Electronic Journal of Statistics 13(1):1166–1211. doi:10.1214/19-EJS1552.
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 mean absolute percentage error.
set.seed(12345)
x <- 0.5
y <- rlnorm(n = 100, mean = 0, sdlog = 1)
print(mape(x = x, y = y))
print(mape(x = rep(x = x, times = 100), y = y))