To investigate the impact of private information, Easley, Kiefer, O'Hara, and Paperman (1996) designed a (PIN) Probability of informed trading measure that is derived based on the daily number of buyer-initiated trades and the number of seller-initiated trades. The fundamental aspect of their model is to assume that order arrivals follow a Poisson distribution. The following code shows how to generate n random numbers from a Poisson distribution:

import scipy as sp
import matplotlib.pyplot as plt
x=sp.random.poisson(lam=1, size=100)
#plt.plot(x,'o')
a = 5. # shape
n = 1000
s = np.random.power(a, n)
count, bins, ignored = plt.hist(s, bins=30)
x = np.linspace(0, 1, 100)
y = a*x**(a-1.)
normed_y = n*np.diff(bins)[0]*y
plt.plot(x, normed_y)
plt.show()