The Gumbell distribution

Generate the exercise results on the Gumbell distribution

import numpy as np
import scipy as sp
import matplotlib.pyplot as plt


def gumbell_dist(arr):
    return -np.log(-np.log(arr))


years_nb = 21
wspeeds = np.load("sprog-windspeeds.npy")
max_speeds = np.array([arr.max() for arr in np.array_split(wspeeds, years_nb)])
sorted_max_speeds = np.sort(max_speeds)

cprob = (np.arange(years_nb, dtype=np.float32) + 1) / (years_nb + 1)
gprob = gumbell_dist(cprob)
speed_spline = sp.interpolate.UnivariateSpline(gprob, sorted_max_speeds, k=1)
nprob = gumbell_dist(np.linspace(1e-3, 1 - 1e-3, 100))
fitted_max_speeds = speed_spline(nprob)

fifty_prob = gumbell_dist(49.0 / 50.0)
fifty_wind = speed_spline(fifty_prob)

plt.figure()
plt.plot(sorted_max_speeds, gprob, "o")
plt.plot(fitted_max_speeds, nprob, "g--")
plt.plot([fifty_wind], [fifty_prob], "o", ms=8.0, mfc="y", mec="y")
plt.plot([fifty_wind, fifty_wind], [plt.axis()[2], fifty_prob], "k--")
plt.text(35, -1, rf"$V_{{50}} = {fifty_wind:.2f} \, m/s$")
plt.xlabel("Annual wind speed maxima [$m/s$]")
plt.ylabel("Gumbell cumulative probability")
plt.show()