Thanks for this further explanation, which has crossed by my and John Maddock's postings. | -----Original Message----- | From: boost-bounces@lists.boost.org | [mailto:boost-bounces@lists.boost.org] On Behalf Of Topher Cooper | Sent: 14 July 2006 14:46 | To: boost@lists.boost.org | 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 +44 1539561830 & SMS, Mobile +44 7714 330204 & SMS pbristow@hetp.u-net.com