MEfit: Mixed Erlang fit In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

Description

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

Usage

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

Arguments

 p Vector of mixing weights, denoted by α in Verbelen et al. (2015). shape Vector of shape parameters r. theta Scale parameter θ. M Number of mixture components. M_initial Initial value provided for M. When NULL (default), not included in the object.

Details

The rate parameter λ used in Albrecher et al. (2017) is equal to 1/θ.

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

Value

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

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

Examples

 1 2 3 4 5 6 7 8 9 10 11 12 # 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)

Example output

----------------------------------------
Summary of splicing fit
----------------------------------------

const = (0.5, 0.996)

pi = (0.5, 0.496, 0.004)

t0 = 0

t = (1 020, 39 096)

type = (ME, TPa, Pa)

* * * * * * * * * * * * * * * * * * * *

p = (0.65, 0.35)

r = (39, 58)

theta = 16.19

M = 2

* * * * * * * * * * * * * * * * * * * *

gamma = (0.76, 0.64)

endpoint = (39 096, Inf)

ReIns documentation built on July 2, 2020, 4:03 a.m.