# Draw samples from the distribution: mu, sigma = 3., 1. # mean and standard deviation s = np.random.lognormal(mu, sigma, 1000) # Display the histogram of the samples, along with # the probability density function: import matplotlib.pyplot as plt count, bins, ignored = plt.hist(s, 100, normed=True, align='mid') x = np.linspace(min(bins), max(bins), 10000) pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) / (x * sigma * np.sqrt(2 * np.pi))) plt.plot(x, pdf, linewidth=2, color='r') plt.axis('tight') plt.show() # Demonstrate that taking the products of random samples from a uniform # distribution can be fit well by a log-normal probability density function. # Generate a thousand samples: each is the product of 100 random # values, drawn from a normal distribution. b = [] for i in range(1000): a = 10. + np.random.random(100) b.append(np.product(a)) b = np.array(b) / np.min(b) # scale values to be positive count, bins, ignored = plt.hist(b, 100, normed=True, align='center') sigma = np.std(np.log(b)) mu = np.mean(np.log(b)) x = np.linspace(min(bins), max(bins), 10000) pdf = (np.exp(-(np.log(x) - mu)**2 / (2 * sigma**2)) / (x * sigma * np.sqrt(2 * np.pi))) plt.plot(x, pdf, color='r', linewidth=2) plt.show()