Compares a chi-square
distribution with high 'df' (degrees of freedom, ν) with
an (asymptotically) "equivalent" Gaussian:
χ²ν(x) =
Φ[(x - μ) ⁄ σ]
⁄ σ, with (from the chi-square)
μ = ν and σ =
√(2 ν) .
This may be useful if numerical difficulties
arise in calculating the chi-square (for high 'df'), and
indicates the adequacy of the Gaussian approximation,
namely, for confidence intervals. For 'df' = 50, e.g., the
width of a 95 % confidence interval for the Gaussian ('gauR') is
already only slightly greater than the correct chi-square ('chiR'),
with gauR ⁄ chiR = 1.004 (1.000 for 'df' ≥ 346).
If the x-limits are both given 0, they are
automatically adjusted to max(0,
μ - 4 σ) and
μ + 5 σ, μ and σ above.
Draws plots of:
the chi-square; and
the equivalent Gaussian. Confidence interval
shown is for the latter. | 
