ReIns (version 1.0.7)

MEfit: Mixed Erlang fit

Description

Create an S3 object using a Mixed Erlang (ME) fit.

Usage

MEfit(p, shape, theta, M, M_initial = NULL)

Arguments

p

Vector of mixing weights, denoted by \(\alpha\) in Verbelen et al. (2015).

shape

Vector of shape parameters \(r\).

theta

Scale parameter \(\theta\).

M

Number of mixture components.

M_initial

Initial value provided for M. When NULL (default), not included in the object.

Value

An S3 object which contains the input arguments in a list.

Details

The rate parameter \(\lambda\) used in Albrecher et al. (2017) is equal to \(1/\theta\).

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

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

SpliceFit, SpliceFitPareto, SpliceFiticPareto, SpliceFitGPD

Examples

# NOT RUN {
# 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)
# }