On Oct 8, 2009, at 12:53 PM, Albyn Jones wrote:
Maithili
I find it really hard to believe that a beta distribution would be a
reasonable probability model for loss data. There would have to be
an upper bound on the size of losses. What is the process that
generates the data. Is there any natural upper bound? Why is there
a lower bound greater than zero?
In insurance situation there is typically a cap on the covered losses
and there is also typically an amount below which it would not make
sense to offer a policy. So a minimum and a maximum are sensible
assumptions about loss distributions in may real modeling situations.
--
David.
That said, the MLE's would be the min and max, but those will
underestimate the range of a beta. It is an elementary exercise to
see why with the uniform[0,B] (ie beta(1,1)), for which the expected
value of the max of a sample of size n is B*n/(n+1). If you have a
lot of data, this may not bother you. For an arbitrary beta
distribution you would have 4 parameters to estimate... probably
a Bayes estimator would be easiest.
I'll put this one away for an exercise my next math stats course...
albyn
Quoting Maithili Shiva <maithili_sh...@yahoo.com>:
Dear Albyn,
Thanks for your reply.
Yes "A" and "B" are unknown. I was just thinking to assign -
A = min(amounts) and B = max(amounts).
The actual loss data I am dealing with is large. I am trying to fit
some statistical distributions to this data. I already have done
with R code pertaining to many other distributions like Normal,
Weibull, Pareto, Generalized extreme Value distribution etc. So
just want to know how to estimate the parameters if I need to check
whether the Beta distribution fits the loss data.
Is it possible for you to guide me how to estimate A and B or can I
assume A = min(amounts) and B = max(Amounts)
Regards
Maithili
--- On Wed, 7/10/09, Albyn Jones <jo...@reed.edu> wrote:
From: Albyn Jones <jo...@reed.edu>
Subject: Re: [R] Parameters of Beta distribution
To: jlu...@ria.buffalo.edu
Cc: "Maithili Shiva" <maithili_sh...@yahoo.com>, r-h...@r-
project.org, r-help-boun...@r-project.org
Date: Wednesday, 7 October, 2009, 3:30 PM
Are A and B known? That is, are there known upper and lower bounds
for this credit loss data? If not, you need to think about how to
estimate those bounds. Why do you believe the data have a beta
distribution?
albyn
On Wed, Oct 07, 2009 at 09:03:31AM -0400, jlu...@ria.buffalo.edu
wrote:
Rescale your data x to (x-A)/(B-A).
Maithili Shiva <maithili_sh...@yahoo.com>
Sent by: r-help-boun...@r-project.org
10/07/2009 08:39 AM
To
r-help@r-project.org
cc
Subject
[R] Parameters of Beta distribution
Supose I have a data pertaining to credit loss as
amounts <-
c(46839.50,31177.12,35696.69,21192.57,29200.91,42049.64,42422.19,
44976.18, 32135.36,47936.57,27322.91,37359.09,43179.60, 48381.02,
45872.38, 28057.30,44643.83,36156.33,16037.62, 45432.28)
I am trying to fit Beta distribution (two parameters distribution
but
where lower bound and upper bounds are NOT 0 and 1 respectively).
For
this I need to estimate the two parameters of Beta distribution. I
found
some code in VGAM pacakge but it deals with standard Beta
distribution
i.e. lower bound (say A) = 0 and upper bound (say B) = 1.
How do I estimate the parameters of the Beta distribution for
above data
where A and B are not 0's?
Please guide.
Thanking you in advance
Maithili
David Winsemius, MD
Heritage Laboratories
West Hartford, CT
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