Smirnov: The goodness of fit
tech-support Smirnov: The goodness of fit

An interesting analysis could be to build a distribution reference line of professional sommeliers who knows how to drink vodka, and an empirical line of people who love to drink Vodka and then compare statistically how far or close they are to be a professional on drinking Vodka, with this comparison we are going to know who is a fraud and who is close to be a Vodka Pro.  

And yes, The Kolmogorov–Smirnov (K-S test) statistic test quantifies a distance between the empirical distribution function of the sample and the cumulative distribution function of the reference distribution, or between the empirical distribution functions of two samples.

The null distribution of this statistic is calculated under the null hypothesis that the sample is drawn from the reference distribution (in the one-sample case) or that the samples are

drawn from the same distribution (in the two-sample case). 

K-S test

The two-sample K–S test is one of the most useful and general nonparametric methods for comparing two samples, as it is sensitive to differences in both location and shape of the empirical cumulative distribution functions of the two samples.

If you think that the main origin of the Pearson Law is the goodness of fit test, you are correct. Some of the most relevant auditing statistics methods are ruled by the K-S test, for example the Benford Law. 

So for next opportunity please do not allow a nice picture capture your attention and for this context get out of the standar and read carefully next time: Is Smirnov not Smirnoff. 

¿Have you seen the error on the title? 


Source: Wikipedia