Python code for estimating the shape and scale parameters for a two-parameter Weibull distribution. It uses scipy.optimize.fmin to minimize the Likelihood function.

weibull.py

from scipy.stats import exponweib
from scipy.optimize import fmin
import numpy as np

# x is your data array
# returns [shape, scale]

def fitweibull(x):
   def optfun(theta):
      return -np.sum(np.log(exponweib.pdf(x, 1, theta[0], scale = theta[1], loc = 0)))
   logx = np.log(x)
   shape = 1.2 / np.std(logx)
   scale = np.exp(np.mean(logx) + (0.572 / shape))
   return fmin(optfun, [shape, scale], xtol = 0.01, ftol = 0.01, disp = 0)