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Appendix V. Cumulative Gaussian and Chi-Squared Distributions

The chi2 confidence limit is the probability of Chi-squared exceeding the observed value; i.e.,

Equation

where Pp for p degrees of freedom is given by Eq. (30a).

Gaussian Confidence Limits

Let chi2 = [x / sigma]2. Then for nD = 1,

Equation

Thus CL for nD is twice the area under a single Gaussian tail. For example the nD = 1 curve for chi2 = 4 has a value of CL = 0.046. This means that the probability of getting | x| geq 2sigma is 4.6% for a Gaussian distribution.

Figure 10

Figure 10. chi2 Confidence Level vs. chi2 for nD Degrees of Freedom (9).

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