Graphics Reference
In-Depth Information
Figure
.
.
he empirical (solid line) and analytical limited expected value functions (LEVFs) for the
log-normal (dashed line)andPareto(dotted line) distributions for the PCS loss catastrophe data. From
XploRe
he probability plot is constructed in the following way. First, the observations
x
,...,x
n
are ordered from the smallest to the largest: x
()
x
(
n
)
. Next, they
are plotted against their observed cumulative frequency, i.e., the points (the crosses
in Figs.
.
-
.
) correspond to the pairs
ċċċ
x
(
i
)
, F
−
,...,n.If
the hypothesized distribution F adequately describes the data, the plotted points fall
approximately along a straight line. If the plotted points deviate significantly from
a straight line, especially at the ends, then the hypothesized distribution is not ap-
propriate.
Figure.
.
shows a Pareto probability plot of the PCS loss data. Apart from the
twoveryextremeobservations(correspondingtoHurricaneAndrewandNorthridge
Earthquake), the points more or less constitute a straight line, validating the choice
of the Pareto distribution. Figures
.
and
.
present log-normal probability plots
of the PCS data. To this end we applied the standard normal probability plots to the
logarithms of the losses and waiting times, respectively. Figure
.
suggests that the
log-normal distribution for the loss severity is not the best choice, whereas Fig.
.
justifies the use of that particular distribution for the waiting time data. Figure
.
depictsanexponential probability plotof thelatter dataset. Wecan see that the expo-
nentialdistributionisnotaverygoodcandidatefortheunderlyingdistributionofthe
waiting timedata -thepointsdeviate fromastraightlineatthefarend.Nevertheless,
the deviation is not that large, and the exponential law may be an acceptable model.
i
.
n
,fori
(
([
−
]
))
=
