import numpy as np

import matplotlib.pyplot as plt

# Parameters

alpha $=2$

beta $=4$

# Inverse CDF $($quantile function$)$

def weibull$\_$inv$($u$,$ alpha, beta$)$:

return alpha $*(-$np$.$log$(1-$ u$))**(1/$ beta$)$

# Generate $100$ random variates

u $=$ np$.$random.uniform$(0,1,100)$

x $=$ weibull$\_$inv$($u$,$ alpha, beta$)$

# Plot histogram and density curve

plt$.$hist$($x$,$ bins$=20,$ density$=$True, alpha$=0\mathrm{.}6,$ color$=\text{'}$g$\text{'})$

# Plot the PDF

xmin, xmax $=$ plt$.$xlim$()$

x $=$ np$.$linspace$($xmin$,$ xmax, $100)$

p $=($beta $/$ alpha$)*($x $/$ alpha$)**($beta $-1)*$ np$.$exp$(-($x $/$ alpha$)**$beta$)$

plt$.$plot$($x$,$ p$,\text{'}$k$\text{'},$ linewidth$=2)$

plt$.$show$()$