MEfit function

Mixed Erlang fit

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

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.

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

Returns

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

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

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)