ProbReg {ReIns}R Documentation

Estimator of small tail probability in regression

Description

Estimator of small tail probability 1Fi(q)1-F_i(q) in the regression case where γ\gamma 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 nn observations (from the response variable).

A

Vector of n1n-1 estimates for A(i/n)A(i/n) obtained from ScaleReg.

q

The used large quantile (we estimate P(Xi>q)P(X_i>q)) for qq large).

plot

Logical indicating if the estimates should be plotted as a function of kk, 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

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

with Hk,nH_{k,n} the Hill estimator. Here, it is assumed that we have equidistant covariates xi=i/nx_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 kk.

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.

See Also

QuantReg, ScaleReg, Prob

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)

[Package ReIns version 1.0.14 Index]