Using SciPy, I am trying to reproduce the weibull fit from this question. My fit looks good when I use the genextreme function as follows:
import numpy as np
from scipy.stats import genextreme
import matplotlib.pyplot as plt
data=np.array([37.50,46.79,48.30,46.04,43.40,39.25,38.49,49.51,40.38,36.98,40.00,
38.49,37.74,47.92,44.53,44.91,44.91,40.00,41.51,47.92,36.98,43.40,
42.26,41.89,38.87,43.02,39.25,40.38,42.64,36.98,44.15,44.91,43.40,
49.81,38.87,40.00,52.45,53.13,47.92,52.45,44.91,29.54,27.13,35.60,
45.34,43.37,54.15,42.77,42.88,44.26,27.14,39.31,24.80,16.62,30.30,
36.39,28.60,28.53,35.84,31.10,34.55,52.65,48.81,43.42,52.49,38.00,
38.65,34.54,37.70,38.11,43.05,29.95,32.48,24.63,35.33,41.34])
shape, loc, scale = genextreme.fit(data)
plt.hist(data, normed=True, bins=np.linspace(15, 55, 9))
x = np.linspace(data.min(), data.max(), 1000)
y = genextreme.pdf(x, shape, loc, scale)
plt.plot(x, y, 'c', linewidth=3)
The parameters are: (0.44693977076022462, 38.283622522613214, 7.9180988170857374). The shape parameter is positive, corresponding to the sign of the shape parameter on the Weibull wikipedia page which as I understand to be equivalent to a negative shape parameter in R?
So it seems genextreme decides by itself whether the distribution is Gumbel, Frechet or Weibull. Here it has chosen Weibull.
Now I am trying to reproduce a similar fit with the weibull_min function. I have tried the following based on this post, but the parameters look very different to what I got with genextreme:
weibull_min.fit(data, floc=0)
The parameters now are: (6.4633107529634319, 0, 43.247460728065136)
Is the 0 the shape parameter? Surely it should be positive if the distribution is Weibull?