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From: Paul A Bristow (pbristow_at_[hidden])
Date: 20060714 10:45:44
Thanks for this further explanation, which has crossed by my and John
Maddock's postings.
 Original Message
 From: boostbounces_at_[hidden]
 [mailto:boostbounces_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 chisquare 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 usecase.
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 +44 1539561830 & SMS, Mobile +44 7714 330204 & SMS pbristow_at_[hidden]
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