SpliceFiticPareto {ReIns}

Splicing of mixed Erlang and Pareto for interval censored data

Description

Fit spliced distribution of a mixed Erlang distribution and a Pareto distribution adapted for interval censoring and truncation.

Usage

SpliceFiticPareto(L, U, censored, tsplice, M = 3, s = 1:10, trunclower = 0, 
                  truncupper = Inf, ncores = NULL, criterium = c("BIC", "AIC"), 
                  reduceM = TRUE, eps = 10^(-3), beta_tol = 10^(-5), maxiter = Inf, 
                  cpp = FALSE)

Arguments

L

Vector of length n with the lower boundaries of the intervals for interval censored data or the observed data for right censored data.

U

Vector of length n with the upper boundaries of the intervals.

censored

A logical vector of length n indicating if an observation is censored.

tsplice

The splicing point t.

M

Initial number of Erlang mixtures, default is 3. This number can change when determining an optimal mixed Erlang fit using an information criterion.

s

Vector of spread factors for the EM algorithm, default is 1:10. We loop over these factors when determining an optimal mixed Erlang fit using an information criterion, see Verbelen et al. (2016).

trunclower

Lower truncation point. Default is 0.

truncupper

Upper truncation point. Default is Inf (no upper truncation).

ncores

Number of cores to use when determining an optimal mixed Erlang fit using an information criterion. When NULL (default), max(nc-1,1) cores are used where nc is the number of cores as determined by detectCores.

criterium

Information criterion used to select the number of components of the ME fit and s. One of "AIC" and "BIC" (default).

reduceM

Logical indicating if M should be reduced based on the information criterion, default is TRUE.

eps

Covergence threshold used in the EM algorithm. Default is 10^(-3).

beta_tol

Threshold for the mixing weights below which the corresponding shape parameter vector is considered neglectable (ME part). Default is 10^(-5).

maxiter

Maximum number of iterations in a single EM algorithm execution. Default is Inf meaning no maximum number of iterations.

cpp

Use C++ implementation (cpp=TRUE) or R implementation (cpp=FALSE) of the algorithm. Default is FALSE meaning the plain R implementation is used.

Details

See Reynkens et al. (2017), Section 4.3.2 of Albrecher et al. (2017) and Verbelen et al. (2015) for details. The code follows the notation of the latter. Initial values follow from Verbelen et al. (2016).

Right censored data should be entered as L=l and U=truncupper, and left censored data should be entered as L=trunclower and U=u.

Value

A SpliceFit object.

Author(s)

Tom Reynkens based on R code from Roel Verbelen for fitting the mixed Erlang distribution (without splicing).

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.

Verbelen, R., Antonio, K. and Claeskens, G. (2016). "Multivariate Mixtures of Erlangs for Density Estimation Under Censoring." Lifetime Data Analysis, 22, 429–455.

See Also

SpliceFitPareto, SpliceFitGPD, Splice

Examples

## Not run: 

# Pareto random sample
X <- rpareto(500, shape=2)

# Censoring variable
Y <- rpareto(500, shape=1)

# Observed sample
Z <- pmin(X,Y)

# Censoring indicator
censored <- (X>Y)

# Right boundary
U <- Z
U[censored] <- Inf

# Splice ME and Pareto
splicefit <- SpliceFiticPareto(L=Z, U=U, censored=censored, tsplice=quantile(Z,0.9))



x <- seq(0,20,0.1)

# Plot of spliced CDF
plot(x, pSplice(x, splicefit), type="l", xlab="x", ylab="F(x)")

# Plot of spliced PDF
plot(x, dSplice(x, splicefit), type="l", xlab="x", ylab="f(x)")


# Fitted survival function and Turnbull survival function 
SpliceTB(x, L=Z, U=U, censored=censored, splicefit=splicefit)


# Log-log plot with Turnbull survival function and fitted survival function
SpliceLL_TB(x, L=Z, U=U, censored=censored, splicefit=splicefit)


# PP-plot of Turnbull survival function and fitted survival function
SplicePP_TB(L=Z, U=U, censored=censored, splicefit=splicefit)

# PP-plot of Turnbull survival function and 
# fitted survival function with log-scales
SplicePP_TB(L=Z, U=U, censored=censored, splicefit=splicefit, log=TRUE)

# QQ-plot using Turnbull survival function and fitted survival function
SpliceQQ_TB(L=Z, U=U, censored=censored, splicefit=splicefit)

## End(Not run)