ReIns: SpliceFit – R documentation

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SpliceFit

Splicing fit

Description

Create an S3 object using ME-Pa or ME-GPD splicing fit obtained from SpliceFitPareto, SpliceFiticPareto or SpliceFitGPD.

Usage

SpliceFit(const, trunclower, t, type, MEfit, EVTfit, loglik = NULL, IC = NULL)

Arguments

`const`	Vector of splicing constants or a single splicing constant.
`trunclower`	Lower truncation point.
`t`	Vector of splicing points or a single splicing point.
`type`	Vector of types of the distributions: `"ME"` and then for each fitted EVT distribution: `"Pa"` (Pareto), `"TPa"` (truncated Pareto) or `"GPD"` (GPD).
`MEfit`	`MEfit` object with details on the mixed Erlang fit.
`EVTfit`	`EVTfit` object with details on the EVT fit.
`loglik`	Log-likelihood of the fitted model. When `NULL` (default), not included in the object.
`IC`	Information criteria of the fitted model. When `NULL` (default), not included in the object. This vector should have length 1, 2 or 3 when included.

Details

See Reynkens et al. (2017) and Section 4.3 in Albrecher et al. (2017) for details.

Value

An S3 object containing the above input arguments and values for π, the splicing weights. These splicing weights are equal to

π_1=const_1, π_2=const_2-const_1, ...,π_{l+1}=1-const_l=1-(π_1+...+π_l)

when l≥ 2 and

π_1=const_1, π_2=1-const_1=1-π_1

when l=1, where l is the length of const.

A summary method is available.

Author(s)

Tom Reynkens

References

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

Reynkens, T., Verbelen, R., Beirlant, J. and Antonio, K. (2017). "Modelling Censored Losses Using Splicing: a Global Fit Strategy With Mixed Erlang and Extreme Value Distributions". Insurance: Mathematics and Economics, 77, 65–77.

Verbelen, R., Gong, L., Antonio, K., Badescu, A. and Lin, S. (2015). "Fitting Mixtures of Erlangs to Censored and Truncated Data Using the EM Algorithm." Astin Bulletin, 45, 729–758

Examples

# Create MEfit object
mefit <- MEfit(p=c(0.65,0.35), shape=c(39,58), theta=16.19, M=2)

# Create EVTfit object
evtfit <- EVTfit(gamma=c(0.76,0.64), endpoint=c(39096, Inf))

# Create SpliceFit object
splicefit <- SpliceFit(const=c(0.5,0.996), trunclower=0, t=c(1020,39096), type=c("ME","TPa","Pa"),
                       MEfit=mefit, EVTfit=evtfit)

# Show summary
summary(splicefit)

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