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)
x |
Vector of points to evaluate the CDF or PDF in. |
p |
Vector of probabilities. |
n |
Number of observations. |
splicefit |
A |
log |
Logical indicating if the densities are given as \log(f), default is |
lower.tail |
Logical indicating if the probabilities are of the form P(X≤ x) ( |
log.p |
Logical indicating if the probabilities are given as \log(p), default is |
See Reynkens et al. (2017) and Section 4.3 in Albrecher et al. (2017) for details.
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.
Tom Reynkens with R code from Roel Verbelen for the mixed Erlang PDF, CDF and quantiles.
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.
## 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)
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