Very Low P-values In Python Kolmogorov-smirnov Goodness Of Fit Test

I have a set of data and fit the corresponding histogram by a lognormal distribution. I first calculate the optimal parameters for the lognormal function, and then plot the histogr

Solution 1:

This simply means that your data isn't exactly log-normal. Based on the histogram, you have a lot of data points for the K-S test to use. This means that if your data is evenly slightly different than would be expected based on a log-normal distribution with those parameters, the K-S test will indicate the data isn't drawn from log-normal.

Where is the data from? If it is from an organic source, or any source other than specifically drawing random numbers from a lognormal distribution, I would expect an extremely small p-value, even if the fits looks great. This certainly isn't a problem though as long as the fit is sufficiently good for your purposes.