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)

# }