python scipy.stats.powerlaw negative exponent

Question

I want to supply a negative exponent for the scipy.stats.powerlaw routine, e.g. a=-1.5, in order to draw random samples:

\"\"\"
powerlaw.pdf(x, a) = a * x**(         


        

Answer 1

If you want to generate power-law distribution, you can use a random deviation. You just have to generate a random number between [0,1] and apply the inverse method (Wolfram). In this case, the probability density function is:

p(k) = k^(-gamma)

and y is the variable uniform between 0 and 1.

y ~ U(0,1)

import numpy as np

def power_law(k_min, k_max, y, gamma):
    return ((k_max**(-gamma+1) - k_min**(-gamma+1))*y  + k_min**(-gamma+1.0))**(1.0/(-gamma + 1.0))

Now to generate a distribution, you just have to create an array

nodes = 1000
scale_free_distribution = np.zeros(nodes, float)
k_min = 1.0
k_max = 100*k_min
gamma = 3.0

for n in range(nodes):
    scale_free_distribution[n] = power_law(k_min, k_max,np.random.uniform(0,1), gamma)

This will work to generate a power-law distribution with gamma=3.0, if you want to fix the average of distribution, you have to study Complex Networks cause the k_min depends of k_max and the average connectivity.