Python random.lognormvariate: Log-Normal Distribution

The random.lognormvariate(mu, sigma) function in Python generates random numbers following a log-normal distribution, which is commonly used in financial modeling and natural phenomena analysis.

Understanding Log-Normal Distribution

A log-normal distribution occurs when the logarithm of a variable follows a normal distribution. It's particularly useful when dealing with quantities that can't be negative, like stock prices or particle sizes.

The distribution is defined by two parameters: mu (mean of the log of the distribution) and sigma (standard deviation of the log of the distribution).

Basic Usage

import random

# Generate a random number from log-normal distribution
result = random.lognormvariate(0, 0.5)
print(f"Random value: {result}")

# Generate multiple values
values = [random.lognormvariate(0, 0.5) for _ in range(5)]
print(f"Multiple values: {values}")

Random value: 1.2847392571
Multiple values: [0.9234, 1.5623, 0.8756, 1.3421, 1.1198]

Parameter Effects

The parameters mu and sigma significantly influence the shape of the distribution. Like its cousin the Gaussian distribution, these parameters control the distribution's characteristics.

import random

# Different parameter combinations
print("Small sigma (0.2):")
values1 = [random.lognormvariate(0, 0.2) for _ in range(5)]
print(values1)

print("\nLarge sigma (1.0):")
values2 = [random.lognormvariate(0, 1.0) for _ in range(5)]
print(values2)

print("\nPositive mu (1.0):")
values3 = [random.lognormvariate(1.0, 0.5) for _ in range(5)]
print(values3)

Practical Applications

Log-normal distributions are widely used in various fields. Here's an example simulating stock price movements, which often follow a log-normal distribution.

import random

def simulate_stock_price(initial_price, days, mu, sigma):
    prices = [initial_price]
    for _ in range(days):
        change = random.lognormvariate(mu, sigma)
        new_price = prices[-1] * change
        prices.append(new_price)
    return prices

# Simulate stock prices for 5 days
stock_prices = simulate_stock_price(100, 5, 0, 0.1)
for day, price in enumerate(stock_prices):
    print(f"Day {day}: ${price:.2f}")

Distribution Visualization

To better understand the distribution's shape, we can create a histogram of generated values. This helps in visualizing how the parameters affect the distribution.

import random
import matplotlib.pyplot as plt

# Generate 1000 random values
values = [random.lognormvariate(0, 0.5) for _ in range(1000)]

# Create histogram
plt.hist(values, bins=50)
plt.title('Log-Normal Distribution')
plt.xlabel('Value')
plt.ylabel('Frequency')
plt.show()

Error Handling

When using random.lognormvariate(), it's important to handle potential errors, especially with invalid parameter values. Similar to the gamma distribution, parameter validation is crucial.

import random

def safe_lognormal(mu, sigma):
    try:
        if sigma <= 0:
            raise ValueError("Sigma must be positive")
        return random.lognormvariate(mu, sigma)
    except ValueError as e:
        print(f"Error: {e}")
        return None

# Test with invalid sigma
print(safe_lognormal(0, -1))  # Error case
print(safe_lognormal(0, 0.5))  # Valid case

Performance Considerations

For generating large numbers of random values, consider using NumPy's implementation for better performance, especially when working with statistical analysis.

Conclusion

random.lognormvariate() is a powerful tool for generating random numbers following a log-normal distribution. It's particularly useful in financial modeling, scientific simulations, and natural phenomena analysis.

Understanding the parameters and their effects is crucial for correctly applying this function in your applications. Remember to handle potential errors and consider performance requirements for your specific use case.