contCDF: Continuous CDF from 'MultiQR' object
In jbrowell/ProbCast: Flexible Probabilistic Forecasting

contCDF

R Documentation

Continuous CDF from `MultiQR` object

Description

This function generats a smooth, continuous CDF a given row of a MultiQR object. Interpolation if performed between quantiles and a range of tail models are available for extrapolating beyond beyond the last estimated upper and lower quantile.

Usage

contCDF(
  quantiles,
  kfold = NULL,
  inverse = F,
  method = list(name = "spline", splinemethod = "monoH.FC"),
  tails = list(method = "extrapolate", L = 0, U = 1),
  ...
)

Arguments

`quantiles`	A single-row `MultiQR` object.
`method`	Method of interpolation. See details.
`tails`	Definition of tails. See details.
`...`	extra arguments to `approxfun` or `splinefun`.
`kfolds`	Fold/test label corresponding to `quantiles`.

Details

Interpolation between quantiles may be linear of via smooth splines:

Linear interpolation: method="linear" linear interpolation between quantiles.

Spline interpolation: method=list(name=spline,splinemethod=monoH.FC), where spline method is passed to splinefun. splinefun=monoH.FC is recommended to guarantee monotonically increasing function.

Several options are available for specifying distribution tails beyond the final upper and lower quantiles:

Linear extrapolation: tails=list(method="extrapolate",L,U) value set to L and U for probability levels 0 and 1, respectively. If method="extrapolate_dtail1" then tails are extrapolated to the 50th quantile plus (minus) U (L).

Exponential tails: tails=list(method="exponential",thicknessPL,thicknessPR,ntailpoints=5) the user will either supply user defined thickness parameters for the tail via thicknessPL and thicknessPR. The number of tail quantiles to be estimated is set by ntailpoints, which defaults to 5. Alternatively tails=list(method="exponential",thickparamFunc) where thickparamFunc is a function that takes the q50 as an input and returns the thickness parameter. If method="extrapolate_dtail2" then tails are extrapolated to the highest quantile in quantiles plus U and the lowest quantile in quantiles plus (L). Note that for both alternative options, U should be positive and L should be negative.

Dynamic exponential tails: tails=list(method="dyn_exponential",ntailpoints=5), where the tail shape is conditional on the values for the upper and lower quantile of qrdata. This method currently only supports an input variable scale of [0,1]. The tail shape moves from linear interpolation when the upper/lower quantile is near the boundary for each respective tail, to a conditional exponential shape.

Generalised Pareto Distribution Tails: tails="gpd", scale_r,shape_r, scale_l,shape_l,tail_qs=seq(0.1,2,by=0.1) with left (_l) and right (_r) scale and shape parameters. Quantiles are calculated at points defined by the upper (lower) quantile plus (minus) tail_qs.