[R] Parameters of Beta distribution

[Albyn Jones]

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?

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_shiva at 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 <jones at reed.edu> wrote:
>
>
> From: Albyn Jones <jones at reed.edu>
> Subject: Re: [R] Parameters of Beta distribution
> To: JLucke at ria.buffalo.edu
> Cc: "Maithili Shiva" <maithili_shiva at yahoo.com>,  
> r-help at r-project.org, r-help-bounces at 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, JLucke at ria.buffalo.edu wrote:
>> Rescale your data x to  (x-A)/(B-A).
>>
>>
>>
>>
>> Maithili Shiva <maithili_shiva at yahoo.com>
>> Sent by: r-help-bounces at r-project.org
>> 10/07/2009 08:39 AM
>>
>> To
>> r-help at 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
>>
>>
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