ReIns: ProbGH – R documentation

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ProbGH

Estimator of small exceedance probabilities and large return periods using generalised Hill

Description

Computes estimates of a small exceedance probability P(X>q) or large return period 1/P(X>q) using the generalised Hill estimates for the EVI.

Usage

ProbGH(data, gamma, q, plot = FALSE, add = FALSE, 
       main = "Estimates of small exceedance probability", ...)

ReturnGH(data, gamma, q, plot = FALSE, add = FALSE, 
         main = "Estimates of large return period", ...)

Arguments

`data`	Vector of n observations.
`gamma`	Vector of n-2 estimates for the EVI obtained from `genHill`.
`q`	The used large quantile (we estimate P(X>q) or 1/P(X>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"` for `ProbGH` and `"Estimates of large return period"` for `ReturnGH`.
`...`	Additional arguments for the `plot` function, see `plot` for more details.

Details

See Section 4.2.2 of 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, only returned for `ProbGH`.
`R`	Vector of the corresponding estimates for the return period, only returned for `ReturnGH`.
`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.

Beirlant J., Goegebeur Y., Segers, J. and Teugels, J. (2004). Statistics of Extremes: Theory and Applications, Wiley Series in Probability, Wiley, Chichester.

Beirlant, J., Vynckier, P. and Teugels, J.L. (1996). "Excess Function and Estimation of the Extreme-value Index". Bernoulli, 2, 293–318.

Examples

data(soa)

# Look at last 500 observations of SOA data
SOAdata <- sort(soa$size)[length(soa$size)-(0:499)]

# Hill estimator
H <- Hill(SOAdata)
# Generalised Hill estimator
gH <- genHill(SOAdata, H$gamma)

# Exceedance probability
q <- 10^7
ProbGH(SOAdata, gamma=gH$gamma, q=q, plot=TRUE)

# Return period
q <- 10^7
ReturnGH(SOAdata, gamma=gH$gamma, q=q, 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