mirror of
https://github.com/rasbt/python_reference.git
synced 2024-12-18 00:00:19 +00:00
37 lines
950 B
Python
37 lines
950 B
Python
import numpy as np
|
|
|
|
def comp_theta_mle(d):
|
|
"""
|
|
Computes the Maximum Likelihood Estimate for a given 1D training
|
|
dataset for a Rayleigh distribution.
|
|
|
|
"""
|
|
theta = len(d) / sum([x**2 for x in d])
|
|
return theta
|
|
|
|
def likelihood_ray(x, theta):
|
|
"""
|
|
Computes the class-conditional probability for an univariate
|
|
Rayleigh distribution
|
|
|
|
"""
|
|
return 2*theta*x*np.exp(-theta*(x**2))
|
|
|
|
if __name__ == "__main__":
|
|
training_data = [10, 18, 19, 22, 24, 29, 33, 40, 68]
|
|
theta = comp_theta_mle(training_data)
|
|
|
|
# Plot Probability Density Function
|
|
from matplotlib import pyplot as plt
|
|
|
|
x_range = np.arange(0, 20, 0.1)
|
|
y_range = [likelihood_ray(theta, x) for x in x_range]
|
|
|
|
plt.figure(figsize=(10,8))
|
|
plt.plot(x_range, y_range, lw=2)
|
|
plt.title('Probability density function for the Rayleigh distribution')
|
|
plt.ylabel('p(x)')
|
|
plt.xlabel('random variable x')
|
|
|
|
plt.show()
|