| -----Original Message----- | From: boost-bounces@lists.boost.org | [mailto:boost-bounces@lists.boost.org] On Behalf Of Topher Cooper | Sent: 12 July 2006 14:11 | To: boost@lists.boost.org | Subject: Re: [boost] [math/staticstics/design] How | besttonamestatisticalfunctions? | This brings to mind another function that, though easily derived | would be good to have to allow internal computations less subject to | round-off error. This is a two parameter function that is the | cumulative probability between a lower and an upper | bound. Mathematically this can always be computed as "CDF(x[ub]) - | CDF(x[lb])" (read the square brackets as mathematical subscript | notation) but numerically with very small intervals, you can easily | end up with 0 when you want something close to | "PDF((x[ub]+x[lb])/2)*(x[ub]-x[lb])". An interesting suggestion. John Maddock has been muttering about using Boost.Interval with these functions. It's on his TODO list allegedly ;-) Would this help with the "CDF(x[ub]) - CDF(x[lb])"? And/or allow one to produce "PDF((x[ub]+x[lb])/2)*(x[ub]-x[lb])" using the density/mass/distribution? | You don't need to make any | general guarantee about precision and so could do initial | implementations as the difference of the cumulative functions, but | then go back and do better for individual distributions. | | I don't know any standard term for this off the top of my head. I | would suggest just using a two argument version of whatever is | decided on for the cumulative distribution. So, using my suggested | function name: | | standard_normal.cdf(-1.0, 1.0) | | would return the probability that a random variate with a normal | distribution is within one standard deviation of the mean. | | The only problem I have with this is that if we look at the one | parameter version as being the two parameter version with one | parameter defaulted its the *first* parameter that is | defaulted since: | | dist.cdf(x) = dist.cdf(-INFINITY, x) | | That would suggest using the complementary cdf instead, but that | seems a lot less natural. The language doesn't make this natural :-( Paul --- Paul A Bristow Prizet Farmhouse, Kendal, Cumbria UK LA8 8AB +44 1539561830 & SMS, Mobile +44 7714 330204 & SMS pbristow@hetp.u-net.com