# Boost :

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

| -----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

| 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

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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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