From 2d042f171ce5329d54d22d6636d3df589a2c908f Mon Sep 17 00:00:00 2001
From: rasbt <se.raschka@me.com>
Date: Thu, 1 May 2014 22:42:28 -0400
Subject: [PATCH] poisson distr

---
 useful_scripts/univariate_poisson_pdf.py | 48 ++++++++++++++++++++++++
 1 file changed, 48 insertions(+)
 create mode 100644 useful_scripts/univariate_poisson_pdf.py

diff --git a/useful_scripts/univariate_poisson_pdf.py b/useful_scripts/univariate_poisson_pdf.py
new file mode 100644
index 0000000..30d3ae4
--- /dev/null
+++ b/useful_scripts/univariate_poisson_pdf.py
@@ -0,0 +1,48 @@
+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()