Re: [boost] [math/staticstics/design] How best tonamestatisticalfunctions?

From: Paul A Bristow (pbristow_at_[hidden])
Date: 2006-07-14 10:45:44

Thanks for this further explanation, which has crossed by my and John
Maddock's postings.

|  -----Original Message-----
|  From: boost-bounces_at_[hidden] 
|  [mailto:boost-bounces_at_[hidden]] On Behalf Of Topher Cooper
|  Sent: 14 July 2006 14:46
|  To: boost_at_[hidden]
|  Subject: Re: [boost] [math/staticstics/design] How best 
|  tonamestatisticalfunctions?
|  
|  I'm not sure what you are quoting with your first line, but, of 
|  course, there isn't a single inverse for any distribution.
|  So, given the CDF for the normal distribution we have, lets 
|  say (this is math not any proposal for C++ naming):
|  
|            CDFz[mu, sigma](x) -> P
|  
|  becomes
|  
|           CDFz(x, mu, sigma) -> P
|  
|  The "standard" inverse CDF is then
|  
|           CDF'z(p, mu, sigma) -> x

So how to we find out what is considered "standard" - ask you? consult
Mathemetica's documentation?textbooks..?  Is there agreement on standard?  I
suspect so, but

If this is to be part of C++ Standard, there needs to be a clear
statisticans standard.

|  And one of the others is:
|  
|           CDF'z(x, mu, p) -> sigma

What John called 'ad hoc'?

|  I.e., given that I know a sample was generated from the normal 
|  distribution with mean mu and that the probability that the sample 
|  was greater than a particular precise value, x, is a particular 
|  precise probability, p, then what is the standard deviation, sigma, 
|  for that distribution?
|  
|  This is an important question algebraically.  It allows us to derive 
|  distributions for parameter estimation that we can then use the 
|  inverse cumulative distribution function to give us confidence bounds 
|  for parameters.  For example, given a particular sample drawn from 
|  say, a chi-square distribution, what is the distribution of possible 
|  values for the number of degrees of freedom?
|  
|  There may be situations where a particular distribution 
|  applies where 
|  a numerical inversion around a parameter is called for, but I can't 
|  think of any.  Can you give me a reasonable scenario where these 
|  inverses around the parameters would be widely used?  Lets 
|  have a use-case.

Well, unless I still don't understand, John produced one?

And I've mentioned the 'how many degrees of freedom would be needed for
chosen probability' example?

Knowing whether more measurements (and/or more precise measurements) are
needed is a very common need (not easily met at present, as far as I can
see).

Or are you talking about something different?

Paul

---
Paul A Bristow
Prizet Farmhouse, Kendal, Cumbria UK LA8 8AB
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pbristow_at_[hidden]