Binomial distribution in VMS

[bi3mw]

I have extended the code in the opening post #1 so that it clearly shows the binomial distribution in the generated text (plot). The distribution seems to be correct.
   

  regimen_sanitatis_binomial.txt (Size: 133.08 KB / Downloads: 13)

Code:

import sys import numpy as np import matplotlib.pyplot as plt from scipy.special import comb def calculate_binomial_distribution(n, max_length):     """Calculates a binomial distribution for word lengths."""     k_values = np.arange(1, max_length + 1)     # Calculate the binomial distribution for the formula comb(n, k) * (0.5 ** n)     probabilities = [comb(n, k) * (0.5 ** n) for k in k_values]     # Normalize the distribution     probabilities /= np.sum(probabilities)     return k_values, probabilities def plot_binomial_distribution(n, max_length):     """Visualizes the binomial distribution and overlays the theoretical curve."""     k_values, probabilities = calculate_binomial_distribution(n, max_length)         # Calculate the theoretical binomial curve     theoretical_probabilities = [comb(n, k) * (0.5 ** n) for k in k_values]     theoretical_probabilities /= np.sum(theoretical_probabilities)         plt.figure(figsize=(10, 6))         # Plot the calculated probabilities     plt.bar(k_values, probabilities, width=0.6, edgecolor='black', alpha=0.6, label='Calculated Distribution')         # Plot the theoretical binomial curve     plt.plot(k_values, theoretical_probabilities, 'r--', marker='o', label='Theoretical Distribution')         plt.xlabel('Word Length')     plt.ylabel('Probability')     plt.title(f'Binomial Distribution for n={n}')     plt.legend()     plt.grid(True)     plt.show() def adjust_word_lengths(words, target_distribution):     """Adjusts word lengths to fit the target distribution by truncating or extending words."""     adjusted_words = []     max_word_length = len(target_distribution)     length_bins = np.arange(1, max_word_length + 1)     length_probs = np.array(target_distribution)     for word in words:         current_length = len(word)         target_length = np.random.choice(length_bins, p=length_probs)             # If the target word length is shorter, truncate the word         if target_length < current_length:             adjusted_words.append(word[:target_length])         # If the target word length is longer, extend the word with 'X'         elif target_length > current_length:             adjusted_words.append(word + 'X' * (target_length - current_length))         else:             adjusted_words.append(word)  # If the length matches, keep the word as is     return adjusted_words def process_text(file_path, output_path):     """Reads the text from the file, adjusts word lengths, and writes the modified text to an output file."""     try:         with open(file_path, 'r', encoding='utf-8') as file:             lines = file.readlines()     except FileNotFoundError:         print(f"Error: The file {file_path} was not found.")         sys.exit(1)     except IOError as e:         print(f"Error: An error occurred while reading the file: {e}")         sys.exit(1)     max_word_length = 15  # Set maximum word length     n = 9  # Number of trials for the binomial distribution     # Calculate the binomial distribution     _, target_distribution = calculate_binomial_distribution(n, max_word_length)     adjusted_lines = []     for line in lines:         words = line.split()         adjusted_words = adjust_word_lengths(words, target_distribution)         adjusted_lines.append(' '.join(adjusted_words))     # Write the modified text to the output file     try:         with open(output_path, 'w', encoding='utf-8') as file:             file.write('\n'.join(adjusted_lines))         print(f"Modified text has been written to {output_path}.")     except IOError as e:         print(f"Error: An error occurred while writing the file: {e}")         sys.exit(1) def main():     if len(sys.argv) != 3:         print("Usage: python adjust_word_length.py <input_filename> <output_filename>")         sys.exit(1)     input_file_path = sys.argv[1]     output_file_path = sys.argv[2]         # Optional visualization of the distribution     max_word_length = 15     n = 9     plot_binomial_distribution(n, max_word_length)         # Process the text and write to the output file     process_text(input_file_path, output_file_path) if __name__ == "__main__":     main()

As @RobGea has already noted, the distribution in the VMS seems to fit roughly section by section, but not folio by folio. I can't understand this, because the result for the entire VMS text must come out somehow. Does anyone have an explanation ?