Probability distributions gi(T) for the example of T = χ2, corresponding to different spectral distribution functions f0 (the “true” model underlying the data), f1 (an approximation to f0 based on finite sampling distance Δ), and f2 (an alternative physical model of the spectrum). The calculation is made for 100 degrees of freedom and α = β = 0.025. Thus, 2.5% of the area under g0 is to the right of the dashed vertical line, and 2.5% of the area under g2 is to the left of this same line. Further, 5% of the area under g1 is to the right of the vertical line.
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