Graphics Reference
In-Depth Information
Software
6.2
Visualization tools would not be very useful without adequate sotware. All of meth-
ods discussed in this chapter are demonstrated using two sotware libraries and one
standaloneapplication.heInsurance Library ofXploRe(www.xplore-stat.de)isacol-
lection of quantlets that illustrate various topics related to insurance (Čižek et al.,
). It is accompanied by online, hyperlinked web tutorials that are freely down-
loadable from the Web (www.xplore-stat.de/tutorials/_Xpl_Tutorials.html).
he Ruin Probabilities toolbox for MATLAB is a set of m-functions with a graphi-
caluserinterface(GUI)thatisprimarilycreatedtovisualize riskprocessesandevalu-
ateruinprobabilities(Miśta,
).Itcanbedownloadedfromwww.im.pwr.wroc.pl/
~hugo/stronaHSC/Podstrony/Programy.html.
he SDE-Solver is a standalone application for the Windows environment. It en-
ables the construction and visualization of solutions of stochastic differential equa-
tions (SDEs) with Gaussian, Poisson, and stable random measures (Janicki et al.,
); for SDE modeling concepts, the reader should consult (Kloeden and Platen,
). he graphics make use of quantile lines and density evolution techniques and
introducetheinterestingconceptofinteractiveprobabilitygates,whichgivetheprob-
ability that the simulated process passes through a specified interval at a specified
point in time (for details see Sect.
.
.
). More information about the sotware can
be found at www.math.uni.wroc.pl/~janicki/solver.html.
Fitting Loss and Waiting Time
Distributions
6.3
he derivation of loss and waiting times (interarrival) distributions from insurance
data is not an easy task. here are three basic approaches: empirical, analytical, and
moment-based. heanalytical approach isprobably the one mostoten used inprac-
tice and certainly the one most frequently adopted in the actuarial literature. It re-
duces to finding an analytical expression that fits the observed data well and is easy
to handle (Daykin et al.,
).
Having a large collection of distributions to choose from, we need to narrow our
selection to a single model and a unique parameter estimate. he type of objective
lossdistribution (thewaiting timedistribution can beanalyzed analogously) can eas-
ily be selected by comparing the shapes of the empirical and theoretical mean excess
functions. Goodness-of-fit can be verified by plotting the corresponding limited ex-
pected value functions or drawing probability plots. Finally, the hypothesis that the
modeled random event is governed by a certain loss distribution can be statistically
tested (but is not discussed in this chapter; for a recent review of goodness-of-fit hy-
pothesis testing see Burnecki et al. (
)).
In the following subsections we will apply the abovementioned visual inference
tools to PCS data. hey will narrow our search for the optimal analytical model of
