ReIns (version 1.0.7)

Splice: Spliced distribution

Description

Density, distribution function, quantile function and random generation for the fitted spliced distribution.

Usage

dSplice(x, splicefit, log = FALSE)
pSplice(x, splicefit, lower.tail = TRUE, log.p = FALSE)
qSplice(p, splicefit, lower.tail = TRUE, log.p = FALSE)
rSplice(n, splicefit)

Arguments

x

Vector of points to evaluate the CDF or PDF in.

p

Vector of probabilities.

n

Number of observations.

splicefit

A SpliceFit object, e.g. output from SpliceFitPareto, SpliceFiticPareto or SpliceFitGPD.

log

Logical indicating if the densities are given as \(\log(f)\), default is FALSE.

lower.tail

Logical indicating if the probabilities are of the form \(P(X\le x)\) (TRUE) or \(P(X>x)\) (FALSE). Default is TRUE.

log.p

Logical indicating if the probabilities are given as \(\log(p)\), default is FALSE.

Value

dSplice gives the density function evaluated in \(x\), pSplice the CDF evaluated in \(x\) and qSplice the quantile function evaluated in \(p\). The length of the result is equal to the length of \(x\) or \(p\).

rSplice returns a random sample of length \(n\).

Details

See Reynkens et al. (2017) and Section 4.3 in Albrecher et al. (2017) for 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

VaR, SpliceFit, SpliceFitPareto, SpliceFiticPareto, SpliceFitGPD, SpliceECDF, SpliceLL, SplicePP

Examples

# NOT RUN {
# Pareto random sample
X <- rpareto(1000, shape = 2)

# Splice ME and Pareto
splicefit <- SpliceFitPareto(X, 0.6)



x <- seq(0, 20, 0.01)

# 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)")



p <- seq(0, 1, 0.01)

# Plot of splicing quantiles
plot(p, qSplice(p, splicefit), type="l", xlab="p", ylab="Q(p)")

# Plot of VaR
plot(p, VaR(p, splicefit), type="l", xlab="p", ylab=bquote(VaR[p]))



# Random sample from spliced distribution
x <- rSplice(1000, splicefit)

# }