Scale: Scale estimator

In TReynkens/ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Scale estimator

Description

Computes the estimator for the scale parameter as described in Beirlant et al. (2016).

Usage

Scale(data, gamma = NULL, logk = FALSE, plot = FALSE, add = FALSE, 
      main = "Estimates of scale parameter", ...)

Arguments

data	Vector of n observations.
gamma	Vector of n-1 estimates for the EVI. When NULL (the default value), Hill estimates are computed.
logk	Logical indicating if the estimates are plotted as a function of \log(k) (logk=TRUE) or as a function of k. Default is FALSE.
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 scale parameter".
...	Additional arguments for the plot function, see plot for more details.

Details

The scale estimates are computed based on the following model for the CDF: 1-F(x) = A x^{-1/\gamma}, where A:= C^{1/\gamma} is the scale parameter:

\hat{A}_{k,n}=(k+1)/(n+1) X_{n-k,n}^{1/H_{k,n}}

where H_{k,n} are the Hill estimates.

See Section 4.2.1 of Albrecher et al. (2017) for more details.

Value

A list with following components:

k	Vector of the values of the tail parameter k.
A	Vector of the corresponding scale estimates.
C	Vector of the corresponding estimates for C, see Details.

Author(s)

Tom Reynkens

References

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

Beirlant, J., Schoutens, W., De Spiegeleer, J., Reynkens, T. and Herrmann, K. (2016). "Hunting for Black Swans in the European Banking Sector Using Extreme Value Analysis." In: Jan Kallsen and Antonis Papapantoleon (eds.), Advanced Modelling in Mathematical Finance, Springer International Publishing, Switzerland, pp. 147–166.

See Also

ScaleEPD, Scale.2o, Hill

Examples

data(secura)

# Hill estimator
H <- Hill(secura$size)

# Scale estimator
S <- Scale(secura$size, gamma=H$gamma, plot=FALSE)

# Plot logarithm of scale          
plot(S$k,log(S$A), xlab="k", ylab="log(Scale)", type="l")

TReynkens/ReIns documentation built on Nov. 9, 2023, 1:29 p.m.