Re: Confidence intervall
- To: mathgroup at smc.vnet.net
- Subject: [mg67761] Re: [mg67658] Confidence intervall
- From: János <janos.lobb at yale.edu>
- Date: Thu, 6 Jul 2006 06:54:18 -0400 (EDT)
- References: <200607040556.BAA29746@smc.vnet.net>
- Sender: owner-wri-mathgroup at wolfram.com
On Jul 4, 2006, at 1:56 AM, dh wrote: > > Hello, > I have a problem that I thought should be rather standard, but I am > looking for quit some time for a good answer and I am still at it. > As I > know that this group is read by quite a few knowledgable people I give > it at try. > Background: > -------------------------------------------------------------- > A calibration curve y=f(x) is least square fitted to some calibration > points ci=(xi,yi) where y is a random variable and x is known > A sample is repeatedly measured: ysi, and xs is determind, so that > Mean[ysi] = f[xs] > A confidence interval is searched for xs, taking into account that we > have small sample sizes. > > Ansatz: > By error propagation we get that part of the variance of xs that is > due > to the calibration points: varc and that due to the sample: vars. > confidence intervall: student Sqrt[varc+vars] > where student is the student factor to some confidence level with a > unknwon degree of freedom. > Now the questthe sample size as well as the variance of calibration > and > sample are different. > --------------------------------------------------- > I think the above problem is equivalent to: > get a confidence interval for the sum of two (normal) random > variables > x1,x2 with variances v1,v2 and degree of freedoms:dof1,dof2, where the > variances and degree of freedoms differ. > In the literature I found the approximation of Welch-Satterthwaite > but > I found by simulation that this is far from perfect. > Does anybody know if an accurate solution or a better approximation is > known? > Daniel Huber I vaguely remember to see something similar in Alfred Rényi 's Probability Theory somewhere in one of the problems section. His notification might be unfamiliar to recent researchers. CMU should have his book in the library. János ---------------------------------------------- Trying to argue with a politician is like lifting up the head of a corpse. (S. Lem: His Master Voice)
- References:
- Confidence intervall
- From: dh <dh@metrohm.ch>
- Confidence intervall