The first meaning of non-parametric covers techniques that do not rely on data belonging to any particular distribution. These include, among others:
- distribution free methods, which do not rely on assumptions that the data are drawn from a given probability distribution. As such it is the opposite of parametric statistics. It includes non-parametric statistical models, inference and statistical tests.
- non-parametric statistics (in the sense of a statistic over data, which is defined to be a function on a sample that has no dependency on a parameter), whose interpretation does not depend on the population fitting any parametrized distributions. Statistics based on the ranks of observations are one example of such statistics and these play a central role in many non-parametric approaches.
I can't see the difference between the two cases: distribution free methods, and non-parametric statistics. Do they both not assume the data coming from some distribution? How do they differ?
Thanks and regards!