# 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))
# target probability distribution
def target_cdf(x):
return (x + x**3 + x**5) / 3.0
# cdf for the distribution 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
rv = RVContinuous(support=[0.0, 1.0], cdf=target_cdf)
sim_components = [
Simulation(target_rv=RVContinuous(support=[0.0, 1.0], cdf=cdf,
n=2 * i + 1),
algorithm='inverse',
inv_cdf=inv_cdf) for i in range(3)
]
sim = Simulation(target_rv=rv,
algorithm='composition',
sim_components=sim_components,
probabilties=[1.0 / 3.0] * 3)
sim.generate(sample_size)
sim.compare(file_path='../images/p8a_{}.png'.format(sample_size))
from simulate import RVContinuous, Simulation
# unpack command-line arguments
alpha = float(sys.argv[1])
beta = float(sys.argv[2])
sample_size = int(sys.argv[3])
# target probability distribution
def target_cdf(x, alpha, beta):
try:
return 1.0 - np.exp(-alpha * x**beta)
except:
return 1.0
# inverse of the target distribution
def inv_cdf(y, alpha, beta):
return (-np.log(1 - y) / alpha)**(1.0 / beta)
# simulate and compare
rv = RVContinuous(support=[0.0, np.inf],
cdf=target_cdf,
alpha=alpha,
beta=beta)
sim = Simulation(target_rv=rv, algorithm='inverse', inv_cdf=inv_cdf)
sim.generate(sample_size)
sim.compare(
file_path='../images/p4_{}_{}_{}.png'.format(alpha, beta, sample_size))
