Splice function

Spliced distribution

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

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.

Details

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

Returns

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 $n$.

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 with R code from Roel Verbelen for the mixed Erlang PDF, CDF and quantiles.

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)
## End(Not run)