In goodness-of-fit (gof) tests (COD, R2, X2) to discriminate PDFs, we need their CDFs.
With wind speed, another PDF is by Maximum Entropy Principle or Method, of the form:
$$f(v)=\exp\left\{-a_0 - a_1v - a_2v^2 - a_3v^3\right\},$$ where $a_0, a_1, a_2$ and $a_3$ are Lagrange multipliers to be determined and $v$ the wind speeds. [THAT I CAN DO!!!]
In probability theory, a normalized PDF is such that:
$$I=\int_{0}^{\max\{v\}} f(v)\,dv = 1,$$ where the limits from lowest ($v=0$) to highest ($v=\max \{v\}$).
Furthermore, the CDF is given by: $$\text{CDF} = F(v)=1-I.$$
I used "Green Energy: Basic Concepts and Fundamentals" by Xianguo Li: Pages 82-83 for all of the above. (And many in the literature)
Also, I used the same data (as he did) provided by Gary Johnson (Wind Book) to calibrate my computations for the Lagrange multipliers with his (Prof Li's) and obtained the EXACT curve for Kansas City on page 86.
My problem now is how to obtain the similar curve fig 3.4 on page 88, for the MEP, only.
Any code, and in any programming language, shall be a big bonus for me. NB: I used numerical integration of $f(v)$ in vain! Thank you.