Fitting And Plotting Lognormal

I'm having trouble doing something as relatively simple as: Draw N samples from a gaussian with some mean and variance Take logs to those N samples Fit a lognormal (using stats.l

Solution 1:

In the call to lognorm.fit(), use floc=0, not floc=mu.

(The location parameter of the lognorm distribution simply translates the distribution. You almost never want to do that with the log-normal distribution.)

See A lognormal distribution in python

By the way, you are plotting the PDF of the unsorted sample values, so the plot in the corrected script won't look much different. You might find it more useful to plot the PDF against the sorted values. Here's a modification of your script that creates a plot of the PDF using the sorted samples:

from scipy import stats
import numpy as np
import matplotlib.pyplot as plt
import math


def lognormDrive(mu,variance):
    size = 1000
    sigma = math.sqrt(variance)
    np.random.seed(1)
    gaussianData = stats.norm.rvs(loc=mu, scale=sigma, size=size)
    logData = np.exp(gaussianData)
    shape, loc, scale = stats.lognorm.fit(logData, floc=0)
    print "Estimated mu:", np.log(scale)
    print "Estimated var: ", shape**2
    logData.sort()
    return logData, stats.lognorm.pdf(logData, shape, loc, scale)

x, y = lognormDrive(37, 0.8)
plt.plot(x, y)
plt.grid()
plt.show()

The script prints:

Estimated mu:37.0347152587Estimated var:0.769897988163

and creates the following plot: