# SplicePP: PP-plot with fitted and empirical survival function In ReIns: Functions from "Reinsurance: Actuarial and Statistical Aspects"

## Description

This function plots the fitted survival function of the spliced distribution versus the empirical survival function (determined using the Empirical CDF (ECDF)).

## Usage

 1 2 SplicePP(X, splicefit, x = sort(X), log = FALSE, plot = TRUE, main = "Splicing PP-plot", ...) 

## Arguments

 X Data used for fitting the distribution. splicefit A SpliceFit object, e.g. output from SpliceFitPareto or SpliceFitGPD. x Vector of points to plot the functions at. By default we plot them at the data points. log Logical indicating if minus the logarithms of the survival probabilities are plotted versus each other, default is FALSE. plot Logical indicating if the splicing PP-plot should be made, default is TRUE. main Title for the plot, default is "Splicing PP-plot". ... Additional arguments for the plot function, see plot for more details.

## Details

The PP-plot consists of the points

(1-\hat{F}(x_{i,n}), 1-\hat{F}_{spliced}(x_{i,n})))

for i=1,…,n with n the length of the data, x_{i,n} the i-th smallest observation, \hat{F} the empirical distribution function and \hat{F}_{spliced} the fitted spliced distribution function. The minus-log version of the PP-plot consists of

(-\log(1-\hat{F}(x_{i,n})), -\log(1-\hat{F}_{spliced}(x_{i,n})))).

Use SplicePP_TB for censored data.

See Reynkens et al. (2017) and Section 4.3.1 in Albrecher et al. (2017) for more details.

## Value

A list with following components:

 spp.the Vector of the theoretical probabilities 1-\hat{F}_{spliced}(x_{i,n}) (when log=FALSE) or -\log(1-\hat{F}_{spliced}(x_{i,n})) (when log=TRUE). spp.emp Vector of the empirical probabilities 1-\hat{F}(x_{i,n}) (when log=FALSE) or -\log(1-\hat{F}(x_{i,n})) (when log=TRUE).

Tom Reynkens

## 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

SplicePP_TB, pSplice, ecdf, SpliceFitPareto, SpliceFitGPD, SpliceECDF, SpliceLL, SpliceQQ

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 ## 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) 

### Example output

sh: 1: wc: Permission denied
sh: 1: cannot create /dev/null: Permission denied


ReIns documentation built on July 2, 2020, 4:03 a.m.