SpliceECDF {ReIns} | R Documentation |
Plot of fitted and empirical survival function
Description
This function plots the fitted survival function of the spliced distribution together with the
empirical survival function (determined using the Empirical CDF (ECDF)). Moreover, 100(1-\alpha)\%
confidence bands are added.
Usage
SpliceECDF(x, X, splicefit, alpha = 0.05, ...)
Arguments
x |
Vector of points to plot the functions at. |
X |
Data used for fitting the distribution. |
splicefit |
A |
alpha |
|
... |
Additional arguments for the |
Details
Use SpliceTB
for censored data.
Confidence bands are determined using the Dvoretzky-Kiefer-Wolfowitz inequality (Massart, 1990).
See Reynkens et al. (2017) and Section 4.3.1 in Albrecher et al. (2017) for more details.
Author(s)
Tom Reynkens
References
Albrecher, H., Beirlant, J. and Teugels, J. (2017). Reinsurance: Actuarial and Statistical Aspects, Wiley, Chichester.
Massart, P. (1990). The Tight Constant in the Dvoretzky-Kiefer-Wolfowitz Inequality. Annals of Probability, 18, 1269–1283.
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
SpliceTB
, pSplice
, ecdf
, SpliceFitPareto
, SpliceFitGPD
, SpliceLL
, SplicePP
, SpliceQQ
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)")
# Fitted survival function and empirical survival function
SpliceECDF(x, X, splicefit)
# Log-log plot with empirical survival function and fitted survival function
SpliceLL(x, X, splicefit)
# PP-plot of empirical survival function and fitted survival function
SplicePP(X, splicefit)
# PP-plot of empirical survival function and
# fitted survival function with log-scales
SplicePP(X, splicefit, log=TRUE)
# Splicing QQ-plot
SpliceQQ(X, splicefit)
## End(Not run)