ReIns (version 1.0.10)

MEfit: Mixed Erlang fit

Description

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

Usage

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

Value

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

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.

Author

Tom Reynkens

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

# 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)