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Percent damage distribution

4 messages · diegol, Ben Bolker, Brian Ripley

#
R version: 2.7.0
Running on: WinXP

I am trying to model damage from fire losses (given that the loss occurred).
Since I have the individual insured amounts, rather than sampling dollar
damage from a continuous distribution ranging from 0 to infinity, I want to
sample from a percent damage distribution from 0-100%. One obvious solution
is to use runif(n, min=0, max=1), but this does not seem to be a good idea,
since I would not expect damage to be uniform.

I have not seen such a distribution in actuarial applications, and rather
than inventing one from scratch I thought I'd ask you if you know one, maybe
from other disciplines, readily available in R.

Thank you in advance.

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~~~~~~~~~~~~~~~~~~~~~~~~~~
Diego Mazzeo
Actuarial Science Student
Facultad de Ciencias Econ?micas
Universidad de Buenos Aires
Buenos Aires, Argentina
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diegol <diegol81 <at> gmail.com> writes:
Beta distribution (rbeta(...)) or
logistic-binomial distribution
plogis(rnorm(...)) .

  See e.g. 

Smithson, Michael, and Jay Verkuilen. 2006. A better lemon squeezer?
Maximum-likelihood regression with beta-distributed dependent variables.
Psychological Methods 11, no. 1 (March): 54-71. doi:2006-03820-004.
#
Thank you, Ben.

The beta distribution seems flexible enough. I knew this distribution but
had never seen it in this kind of application, and somehow did not recall
it.
rbeta(n, shape1 = 5, shape2 = 1) looks reasonable to start with for my
simple task. If I had a real dataset I could parameterize it with a standard
method.


Regards,
Diego
Ben Bolker wrote:
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~~~~~~~~~~~~~~~~~~~~~~~~~~
Diego Mazzeo
Actuarial Science Student
Facultad de Ciencias Econ?micas
Universidad de Buenos Aires
Buenos Aires, Argentina
#
Not an R question as yet .....

In my limited experience (we have some insurance projets), 100% can occur, 
but otherwise a beta distbribution may suit, which suggests a mixture 
distribution.  But start with an empirical examination (histogram, ecdf, 
density plot) of the distribution, since it may reveal other features.

The next question is 'why model'?   For such a simple problem (a 
univariate distribution) a plot may be a sufficent analysis, and for e.g. 
simulation you could just re-sample the data.
On Thu, 25 Dec 2008, diegol wrote: