Computes a
Weibull distribution, as a test for graph behaviour.
Namely, it observes 'gnuplot's "filledcurves".
For the Weibull distribution, it is
μ = λ Γ(1 + 1 ⁄k),
σ² = λ
[Γ(1 + 2 ⁄k) −
Γ²(1 + 1 ⁄k)],
and the mode is λ
[(k−1)⁄k]1⁄k.
This is a simple test to consolidate 'gnuplot'
graphs. Accessorily, in the 2.nd plot,
the progressive trapezoidal and Simpson's rules are used,
i.e., each value of the numerical integrals
is computed from the previous one. For the trapezoidal, it is:
Ik = Ik−1 +
1⁄2 (fk−1 + fk),
with the integral
I Δx ⁄ 2 .
For the Simpson's, it is:
Ik⁄2 =
Ik⁄2−1 +
fk−2 + 4 fk−1 + fk,
with the integral
I Δx ⁄ 3 .
(This is not visible from the Wikipedia references below or,
to our knowledge, any others, except Casquilho [2010].)
Draws plots for (1) the Weibull 'pdf',
(2) the shaded left and right "significance", and
(3) the Weibull 'cdf'. |
• Wikipedia: Weibull distribution • Wikipedia: Trapezoidal rule.
• Casquilho, M.,
2010, "Numerical integration in tabular form", ICEE-2010,
International Conference on Engineering Education,
Gliwice, Poland, 18–22 Jul..
• 1798-09-11: Neumann, Franz Ernst
(† 1895-05-23). |
