Simulates samples
of given size, n, to build the correspondng experimental
curves of the Student's t and of χ² (chi-square)
distributions. For the latter, the two tails are made equal, as usual
(not minimized), as the practical difference is possibly negligible.
Graphs are drawn for:
Student's (i) t pdf, (ii) simulated t,
(iii) t cdf, and (iv) simulated cumul. t;
χ² (i) pdf, (ii) simulated χ²,
(iii) χ² cdf,
and (iv) simulated cumul. χ².
Asymptotically: t tends to the standard Gaussian
(with peak going from ~0.36 to Gaussian ~0.39
[1⁄ √(2π) =
1⁄ ~2.5]; and
χ² tends to Gaussian
(μ=df; σ=√(2 df)),
df = n − 1.
The "symmetric" shaded probabilities are also shown. |
