python - scipy, lognormal distribution - parameters

Question

I want to fit lognormal distribution to my data, using python scipy.stats.lognormal.fit. According to the manual, fit returns shape, loc, scale parameters. But, lognormal distribution normally needs only two parameters: mean and standard deviation.

How to interpret the results from scipy fit function? How to get mean and std.dev.?

Answer 1

The distributions in scipy are coded in a generic way wrt two parameter location and scale so that location is the parameter (loc) which shifts the distribution to the left or right, while scale is the parameter which compresses or stretches the distribution.

For the two parameter lognormal distribution, the "mean" and "std dev" correspond to log(scale) and shape (you can let loc=0).

The following illustrates how to fit a lognormal distribution to find the two parameters of interest:

In [56]: import numpy as np

In [57]: from scipy import stats

In [58]: logsample = stats.norm.rvs(loc=10, scale=3, size=1000) # logsample ~ N(mu=10, sigma=3)

In [59]: sample = np.exp(logsample) # sample ~ lognormal(10, 3)

In [60]: shape, loc, scale = stats.lognorm.fit(sample, floc=0) # hold location to 0 while fitting

In [61]: shape, loc, scale
Out[61]: (2.9212650122639419, 0, 21318.029350592606)

In [62]: np.log(scale), shape  # mu, sigma
Out[62]: (9.9673084420467362, 2.9212650122639419)