SpliceFit {ReIns}

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 \pi, the splicing weights. These splicing weights are equal to

\pi_1=const_1, \pi_2=const_2-const_1, ...,\pi_{l+1}=1-const_l=1-(\pi_1+...+\pi_l)

when l\ge 2 and

\pi_1=const_1, \pi_2=1-const_1=1-\pi_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

See Also

MEfit, EVTfit, SpliceFitPareto, SpliceFiticPareto, SpliceFitGPD

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)