python_reference/useful_scripts/univariate_poisson_pdf.py

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2014-05-02 02:42:28 +00:00
import numpy as np
import math
def poisson_lambda_mle(d):
"""
Computes the Maximum Likelihood Estimate for a given 1D training
dataset from a Poisson distribution.
"""
return sum(d) / len(d)
def likelihood_poisson(x, lam):
"""
Computes the class-conditional probability for an univariate
Poisson distribution
"""
if x // 1 != x:
likelihood = 0
else:
likelihood = math.e**(-lam) * lam**(x) / math.factorial(x)
return likelihood
if __name__ == "__main__":
# Plot Probability Density Function
from matplotlib import pyplot as plt
training_data = [0, 1, 1, 3, 1, 0, 1, 2, 1, 2, 2, 1, 2, 0, 1, 4]
mle_poiss = poisson_lambda_mle(training_data)
true_param = 1.0
x_range = np.arange(0, 5, 0.1)
y_true = [likelihood_poisson(x, true_param) for x in x_range]
y_mle = [likelihood_poisson(x, mle_poiss) for x in x_range]
plt.figure(figsize=(10,8))
plt.plot(x_range, y_true, lw=2, alpha=0.5, linestyle='--', label='true parameter ($\lambda={}$)'.format(true_param))
plt.plot(x_range, y_mle, lw=2, alpha=0.5, label='MLE ($\lambda={}$)'.format(mle_poiss))
plt.title('Poisson probability density function for the true and estimated parameters')
plt.ylabel('p(x|theta)')
plt.xlim([-1,5])
plt.xlabel('random variable x')
plt.legend()
plt.show()