SpliceFit function

Splicing fit

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

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.

Returns

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

when $l\ge 2$ and

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

A summary method is available.

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

Author(s)

Tom Reynkens

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)