Description Usage Arguments Value Author(s) References Examples

Functions to compute the analytical expressions in Table 3 of the paper by Ehm et al (2016). These expressions yield the expected score of various forecasters, given the synthetic setup studied in Section 3.3 and Appendix B of the paper. The expressions can be used to replicate Figure 2 in the paper.

1 2 | ```
expected_score_mean(theta, forecaster = "P")
expected_score_quantile(theta, alpha, forecaster = "P")
``` |

`theta` |
Value of the parameter $theta$, indexing the extremal score |

`alpha` |
Quantile level, between zero and one |

`forecaster` |
ID of the forecaster, string of length one. Either "P" (perfect forecaster), "C" (climatological forecaster), "U" (unfocused forecaster), or "SR" (sign-reversed forecaster). |

Expected value of the extremal score, given the synthetic setup described in Section 3.3 of Ehm et al (2016).

Alexander Jordan, 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).

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 | ```
## Not run:
# Color palette, obtained from http://www.cookbook-r.com/Graphs/Colors_
cbbPalette <- c("#000000", "#E69F00", "#56B4E9", "#009E73")
cbbPalette <- cbbPalette[c(1, 4, 2, 3)]
# Labeling stuff
forecasters <- c("P", "C", "U", "SR")
names <- c("Perfect", "Climatological", "Unfocused", "Sign-Reversed")
x_label <- expression(paste("Parameter ", theta))
# Figure 2, top left
# Grid for theta
theta_grid1 <- seq(-3, 3, 0.01)
# Expected scores for all forecasters
scores1 <- sapply(forecasters, expected_score_mean, theta = theta_grid1)
# Plot
matplot(x = theta_grid1, y = scores1[, 4:1], type = "l", lty = 1, col = cbbPalette[4:1],
lwd = 2, bty = "n", xlab = x_label, ylab = expression("Expected Score"))
legend("topright", names, col = cbbPalette, lwd = 2, bty = "n")
## End(Not run)
``` |

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