# target probability distribution
def target_cdf(x, *args):
return sum([a * x**(i + 1) for i, a in enumerate(alpha)])
# distribution for x^n
def cdf(y, n):
return x**n
# inverse for the distribution x^n
def inv_cdf(y, n):
return y**(1.0 / n)
# simulate and compare
sim_components = [
Simulation(RVContinuous(support=[0.0, 1.0], cdf=cdf, n=i + 1),
algorithm='inverse',
inv_cdf=inv_cdf) for i in range(degree)
]
rv = RVContinuous(support=[0.0, 1.0], cdf=target_cdf)
sim = Simulation(target_rv=rv,
algorithm='composition',
sim_components=sim_components,
probabilties=alpha)
sim.generate(sample_size)
sim.compare(file_path='../images/p8c_{}_{}.png'.format(degree, sample_size))
print('The generated probability weights are:\n{}'.format(alpha))
import numpy as np
from simulate import RVContinuous, Simulation
# a useful constant
c = 1.0 - np.exp(-0.05)
# target probability distribution
def target_cdf(x):
return (1.0 - np.exp(-x)) / c
# inverse of the target distribution
def inv_cdf(y):
return -np.log(1.0 - c * y)
# simulate and compare
rv = RVContinuous(support=[0.0, 0.05], cdf=target_cdf)
sim = Simulation(target_rv=rv, algorithm='inverse', inv_cdf=inv_cdf)
sim.generate(1000)
sim.compare(file_path='../images/p6.png')
print('simulated mean = {:.4f}\nexact mean = {:.4f}'.format(
sim.mean, sim.rv.mean))