from matplotlib.pyplot import *
from numpy import linspace, exp

def calc_frechet_pdf(x,a,s):
    y = (a/s) * ((x/s)**(-1-a)) * exp(- (x/s)**(-a) )
    return y
 
x = linspace(0,4,10**5)
 
fig = figure()
ax = fig.add_subplot(111)
ax.plot(x,calc_frechet_pdf(x,1.,1.),label=r'$\alpha=1;$ $s=1$', linewidth=2)
ax.plot(x,calc_frechet_pdf(x,2.,1.),label=r'$\alpha=2;$ $s=1$', linewidth=2)
ax.plot(x,calc_frechet_pdf(x,3.,1.),label=r'$\alpha=3;$ $s=1$', linewidth=2)
ax.plot(x,calc_frechet_pdf(x,1.,2.),label=r'$\alpha=1;$ $s=2$', linewidth=2)
ax.plot(x,calc_frechet_pdf(x,2.,2.),label=r'$\alpha=2;$ $s=2$', linewidth=2)
ax.plot(x,calc_frechet_pdf(x,3.,2.),label=r'$\alpha=3;$ $s=2$', linewidth=2)
ax.grid(True)
ax.minorticks_on()
ax.legend(loc=1)
ax.set_xlim(0,4)
ax.set_ylim(0,1.5)
ax.set_xlabel("x")
ax.set_ylabel("PDF")
fig.savefig("Frechet_pdf.svg",bbox_inches="tight", pad_inches=.15)

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