from __future__ import division
import numpy as np
import matplotlib.pyplot as plt

def qexp(x,q):
 
    if q == 1:
        y = np.exp(x)
    else:
        y = (1+(1-q)*x)**(1/(1-q))
     
    y[ 1+(1-q)*x <=0 ] = 0
    
    return y
step = 0.001
X = np.arange(0, 2.5, step)
 
col = {1: 'orange', 2: 'purple', 3: 'lightblue', 4:'pink'}
 
                                                                             
plt.figure(figsize=(4,3.2))
plt.axes([0.17,0.13,0.79,0.8])
plt.hold(True)

A = []
leg_str = []
lvals = [1, 1, 1, 0.5]
qvals = [0, 0, 1, 1.5]
kvals = [1,2,2,1]
for i,q,k,l in zip(range(qvals.__len__()),qvals,kvals,lvals):
    b = 1-(1-q)*(X/l)**k
    P = (2-q)*k/l*(X/l)**(k-1)*qexp(-(X/l)**k,q)
    integral = sum(P)*step
    a, = plt.plot(X, P, '-', color=col[i+1],lw =2.5)
    A.append(a)
    leg_str.append(r"$\kappa={k},q={q},\lambda={l}$".format(k=k, q=q, l=l))
 
 
plt.xlabel("x")
plt.ylabel(r"P(x)")

bx = plt.legend(A, leg_str,numpoints=1, handletextpad=0, loc="upper right")
bx.draw_frame(False)
 
plt.savefig("qWeibull_pdf.svg")