Description Usage Arguments Value Author(s) References

Implementations of some scoring functions discussed in the paper.

1 2 3 4 | ```
extremal_score(x, y, theta, functional = "expectile", alpha = 0.5)
apl_score(x, y, alpha = 0.5)
ase_score(x, y, alpha = 0.5)
``` |

`x` |
Numeric vector of forecasts |

`y` |
Numeric vector of realizations (same length as |

`theta` |
Threshold parameter for extremal score (must be a numeric scalar) |

`functional` |
String, either "expectile" or "quantile" |

`alpha` |
Level of the quantile or expectile, must be a numeric scalar in the (0,1) interval |

All functions return a vector of scores (same length as `x`

and `y`

). Smaller scores correspond to better forecasts.

`extremal_score`

is the scoring function defined in Equations (10) and (12) of Ehm et al (2016). `apl_score`

is the asymmetric piecewise scoring function for quantiles, see Equation (6) in Ehm et al (2016). `ase_score`

is the asymmetric squared error for expectiles, see Equation (8) in Ehm et al (2016).

Fabian Krueger

Ehm, W., Gneiting, T., Jordan, A. and Krueger, F. (2016): Of Quantiles and Expectiles: Consistent Scoring Functions, Choquet Representations, and Forecast Rankings. *Journal of the Royal Statistical Society (Series B)* 78, 1-29. doi: 10.1111/rssb.12154 (open access).

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