ReIns: Prob – R documentation

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Prob

Weissman estimator of small exceedance probabilities and large return periods

Description

Compute estimates of a small exceedance probability P(X>q) or large return period 1/P(X>q) using the approach of Weissman (1978).

Usage

Prob(data, gamma, q, plot = FALSE, add = FALSE, 
     main = "Estimates of small exceedance probability", ...)
          
Return(data, gamma, q, plot = FALSE, add = FALSE, 
       main = "Estimates of large return period", ...)
        
Weissman.p(data, gamma, q, plot = FALSE, add = FALSE, 
           main = "Estimates of small exceedance probability", ...)
          
Weissman.r(data, gamma, q, plot = FALSE, add = FALSE, 
           main = "Estimates of large return period", ...)

Arguments

`data`	Vector of n observations.
`gamma`	Vector of n-1 estimates for the EVI, typically Hill estimates are used.
`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 extreme quantile"` for `Prob` and `"Estimates of large return period"` for `Return`.
`...`	Additional arguments for the `plot` function, see `plot` for more details.

Details

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

Weissman.p and Weissman.r are the same functions as Prob and Return but with a different name for compatibility with the old S-Plus code.

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 `Prob`.
`R`	Vector of the corresponding estimates for the return period, only returned for `Return`.
`q`	The used large quantile.

Author(s)

Tom Reynkens based on S-Plus code from Yuri Goegebeur.

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.

Weissman, I. (1978). "Estimation of Parameters and Large Quantiles Based on the k Largest Observations." Journal of the American Statistical Association, 73, 812–815.

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)

# Exceedance probability
q <- 10^6
# Weissman estimator
Prob(SOAdata,gamma=H$gamma,q=q,plot=TRUE)

# Return period
q <- 10^6
# Weissman estimator
Return(SOAdata,gamma=H$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