Create normal_distribution.py

tools/normal_distribution.py

@@ -0,0 +1,80 @@
+import random
+import math
+import matplotlib.pyplot as plt
+
+def generate_normal_distribution(mean: float, std_dev: float, count: int = 10000)->list:
+    """Generate a list of random numbers from a normal distribution.
+
+    This function generates a list of random numbers drawn from a normal 
+    distribution specified by the mean and standard deviation.
+
+    Args:
+        mean: The mean (average) of the normal distribution.
+        std_dev: The standard deviation of the normal distribution.
+        count: The number of random samples to generate (default: 10000).
+
+    Returns:
+        list: A list of samples drawn from the specified normal distribution.
+    """
+    samples = []
+
+    for _ in range(count // 2):  # Generate pairs of samples
+        u1 = random.random()
+        u2 = random.random()
+        
+        # Box-Muller transform
+        z0 = math.sqrt(-2.0 * math.log(u1)) * math.cos(2.0 * math.pi * u2)
+        z1 = math.sqrt(-2.0 * math.log(u1)) * math.sin(2.0 * math.pi * u2)
+
+        # Scale and shift to the specified mean and standard deviation
+        samples.append(z0 * std_dev + mean)
+        samples.append(z1 * std_dev + mean)
+
+    return samples
+
+def create_histogram_and_theorical_pdf(mean: float, std_dev:float, random_numbers:list)->None:
+    """Generate a histogram of random numbers and overlay the theoretical 
+    probability density function (PDF) of a normal distribution. 
+    Return the histogram as a base64-encoded string.
+
+    Args:
+        mean: The mean (average) of the normal distribution.
+        std_dev: The standard deviation of the normal distribution.
+        random_numbers: A list of random numbers generated from a 
+                                         normal distribution.
+    """
+    # Prepare data for plotting
+    hist_data = [0] * 50  # Create a list to hold histogram data
+    min_value = min(random_numbers)
+    max_value = max(random_numbers)
+    bin_width = (max_value - min_value) / len(hist_data)
+
+    # Fill histogram data
+    for number in random_numbers:
+        bin_index = int((number - min_value) / bin_width)
+        if bin_index >= len(hist_data):
+            bin_index = len(hist_data) - 1
+        hist_data[bin_index] += 1
+
+    # Normalize histogram data
+    hist_data = [count / len(random_numbers) / bin_width for count in hist_data]
+
+    # Prepare x values for the theoretical PDF
+    x_values = [min_value + i * bin_width for i in range(len(hist_data))]
+
+    # Calculate the corresponding y values for the theoretical normal distribution
+    pdf_values = [
+        (1 / (std_dev * math.sqrt(2 * math.pi))) * math.exp(-0.5 * ((x - mean) / std_dev) ** 2) \
+            for x in x_values
+    ]
+
+    # Plotting
+    plt.figure(figsize=(10, 6))
+    plt.bar(x_values, hist_data, width=bin_width, alpha=0.6, color='g', label='Histogram')
+    plt.plot(x_values, pdf_values, 'k', linewidth=2, label='Theoretical PDF')
+
+    plt.title(f'Histogram of {len(random_numbers)} Random Numbers\nMean: {mean}, Std Dev: {std_dev}')
+    plt.xlabel('Value')
+    plt.ylabel('Density')
+    plt.legend()
+    plt.grid()