ReIns: SpliceQQ – R documentation

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SpliceQQ

Splicing quantile plot

Description

Computes the empirical quantiles of a data vector and the theoretical quantiles of the fitted spliced distribution. These quantiles are then plotted in a splicing QQ-plot with the theoretical quantiles on the x-axis and the empirical quantiles on the y-axis.

Usage

SpliceQQ(X, splicefit, p = NULL, plot = TRUE, main = "Splicing QQ-plot", ...)

Arguments

`X`	Vector of n observations.
`splicefit`	A `SpliceFit` object, e.g. output from `SpliceFitPareto` or `SpliceFitGPD`.
`p`	Vector of probabilities used in the QQ-plot. If `NULL`, the default, we take `p` equal to `1/(n+1),...,n/(n+1)`.
`plot`	Logical indicating if the quantiles should be plotted in a splicing QQ-plot, default is `TRUE`.
`main`	Title for the plot, default is `"Splicing QQ-plot"`.
`...`	Additional arguments for the `plot` function, see `plot` for more details.

Details

This QQ-plot is given by

(Q(p_j), \hat{Q}(p_j)),

for j=1,…,n where Q is the quantile function of the fitted splicing model and \hat{Q} is the empirical quantile function and p_j=j/(n+1).

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

Value

A list with following components:

`sqq.the`	Vector of the theoretical quantiles of the fitted spliced distribution.
`sqq.emp`	Vector of the empirical quantiles from the data.

Author(s)

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

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)

ReIns

Functions from "Reinsurance: Actuarial and Statistical Aspects"

v1.0.10

GPL (>= 2)

Authors

Tom Reynkens [aut, cre] (<https://orcid.org/0000-0002-5516-5107>), Roel Verbelen [aut] (R code for Mixed Erlang distribution, <https://orcid.org/0000-0002-2347-9240>), Anastasios Bardoutsos [ctb] (Original R code for cEPD estimator), Dries Cornilly [ctb] (Original R code for EVT estimators for truncated data), Yuri Goegebeur [ctb] (Original S-Plus code for basic EVT estimators), Klaus Herrmann [ctb] (Original R code for GPD estimator)

Initial release

2020-05-16