rayl

useful_scripts/univariate_rayleigh_pdf.py

@@ -0,0 +1,36 @@
+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()