Why do the Frechet distributions differ in scipy.stats vs R

Question

I've fitted a frechet distribution in R and would like to use this in a python script. However inputting the same distribution parameters in scipy.stats.frechet_r gives me a very different curve. Is this a mistake in my implementation or a fault in scipy ?

R distribution:

vs Scipy distribution:

R frechet parameters: loc=17.440, shape=0.198, scale=8.153

python code:

from scipy.stats import frechet_r
import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots(1, 1)

F=frechet_r(loc=17.440  ,scale= 8.153, c=   0.198)              
x=np.arange(0.01,120,0.01)
ax.plot(x, F.pdf(x), 'k-', lw=2)

plt.show()

edit - relevant documentation.

The Frechet parameters were calculated in R using the fgev function in the 'evd' package http://cran.r-project.org/web/packages/evd/evd.pdf (page 40)

Link to the scipy documentation: http://docs.scipy.org/doc/scipy/reference/generated/scipy.stats.frechet_r.html#scipy.stats.frechet_r

Answer 1

I haven't used the frechet_r function from scipy.stats (when just quickly testing it I got the same plot out as you) but you can get the required behaviour from genextreme in scipy.stats. It is worth noting that for genextreme the Frechet and Weibull shape parameter have the 'opposite' sign to usual. That is, in your case you would need to use a shape parameter of -0.198:

from scipy.stats import genextreme as gev
import matplotlib.pyplot as plt
import numpy as np
fig, ax = plt.subplots(1, 1)

x=np.arange(0.01,120,0.01)
# The order for this is array, shape, loc, scale
F=gev.pdf(x,-0.198,loc=17.44,scale=8.153)

plt.plot(x,F,'g',lw=2)
plt.show()