Hyndman–Fan Taxonomy
Presented in hyndman1996.
| Type | h | Equation |
|---|---|---|
| 1 | $np$ | $x_{(\hc)}$ |
| 2 | $np+1/2$ | $(x_{(\lceil h - 1/2 \rceil)} + x_{(\lceil h + 1/2 \rceil)})/2$ |
| 3 | $np$ | $x_{(\hr)}$ |
| 4 | $np$ | $x_{(\hf)}+(h-\hf)(x_{(\hc)} - x_{(\hf)})$ |
| 5 | $np+1/2$ | $x_{(\hf)}+(h-\hf)(x_{(\hc)} - x_{(\hf)})$ |
| 6 | $(n+1)p$ | $x_{(\hf)}+(h-\hf)(x_{(\hc)} - x_{(\hf)})$ |
| 7 | $(n-1)p+1$ | $x_{(\hf)}+(h-\hf)(x_{(\hc)} - x_{(\hf)})$ |
| 8 | $(n+1/3)p+1/3$ | $x_{(\hf)}+(h-\hf)(x_{(\hc)} - x_{(\hf)})$ |
| 9 | $(n+1/4)p+3/8$ | $x_{(\hf)}+(h-\hf)(x_{(\hc)} - x_{(\hf)})$ |
Table : The Hyndman–Fan taxonomy of quantile estimators