ReIns: ProbReg – R documentation

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ProbReg

Estimator of small tail probability in regression

Description

Estimator of small tail probability 1-F_i(q) in the regression case where γ is constant and the regression modelling is thus only solely placed on the scale parameter.

Usage

ProbReg(Z, A, q, plot = FALSE, add = FALSE, 
        main = "Estimates of small exceedance probability", ...)

Arguments

`Z`	Vector of n observations (from the response variable).
`A`	Vector of n-1 estimates for A(i/n) obtained from `ScaleReg`.
`q`	The used large quantile (we estimate P(X_i>q)) for q large).
`plot`	Logical indicating if the estimates should be plotted as a function of k, default is `FALSE`.
`add`	Logical indicating if the estimates should be added to an existing plot, default is `FALSE`.
`main`	Title for the plot, default is `"Estimates of small exceedance probability"`.
`...`	Additional arguments for the `plot` function, see `plot` for more details.

Details

The estimator is defined as

1-\hat{F}_i(q) = \hat{A}(i/n) (k+1)/(n+1) (q/Z_{n-k,n})^{-1/H_{k,n}},

with H_{k,n} the Hill estimator. Here, it is assumed that we have equidistant covariates x_i=i/n.

See Section 4.4.1 in Albrecher et al. (2017) for more details.

Value

A list with following components:

`k`	Vector of the values of the tail parameter k.
`P`	Vector of the corresponding probability estimates.
`q`	The used large quantile.

Author(s)

Tom Reynkens.

References

Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.

Examples

data(norwegianfire)

Z <- norwegianfire$size[norwegianfire$year==76]

i <- 100
n <- length(Z)

# Scale estimator in i/n
A <- ScaleReg(i/n, Z, h=0.5, kernel = "epanechnikov")$A

# Small exceedance probability
q <- 10^6
ProbReg(Z, A, q, plot=TRUE)

# Large quantile
p <- 10^(-5)
QuantReg(Z, A, p, plot=TRUE)

ReIns

Functions from "Reinsurance: Actuarial and Statistical Aspects"

v1.0.10

GPL (>= 2)

Authors

Tom Reynkens [aut, cre] (<https://orcid.org/0000-0002-5516-5107>), Roel Verbelen [aut] (R code for Mixed Erlang distribution, <https://orcid.org/0000-0002-2347-9240>), Anastasios Bardoutsos [ctb] (Original R code for cEPD estimator), Dries Cornilly [ctb] (Original R code for EVT estimators for truncated data), Yuri Goegebeur [ctb] (Original S-Plus code for basic EVT estimators), Klaus Herrmann [ctb] (Original R code for GPD estimator)

Initial release

2020-05-16