The 2 confidence limit is the probability of Chi-squared exceeding the observed value; i.e.,
where Pp for p degrees of freedom is given by Eq. (30a).
Gaussian Confidence Limits
Let 2 = [x / ]2. Then for nD = 1,
Thus CL for nD is twice the area under a single Gaussian tail. For example the nD = 1 curve for 2 = 4 has a value of CL = 0.046. This means that the probability of getting | x| 2 is 4.6% for a Gaussian distribution.
Figure 10. 2 Confidence Level vs. 2 for nD Degrees of Freedom (9).