Nonparametric Method/Examples

Examples of Nonparametric Methods

Arbitrary Example $1$

Suppose we have random samples from two populations with unspecified cumulative distribution functions $\map F x$ and $\map G x$.

A test for:

the hypothesis $\map F x = \map G x$ for all $x$

against:

the alternative hypothesis that $\map F x < \map G x$ for all $x$

would be a test that is both nonparametric and distribution-free.

Arbitrary Example $2$

Suppose we have random samples from two populations with unspecified cumulative distribution functions $\map F x$ and $\map G x$.

A test for:

the hypothesis $\map G x = \map F x$ for all $x$

against:

the alternative hypothesis that $\map G x < \map F {x - \theta}$ for all $x$, where $\theta$ is some parameter

would be a test that is distribution-free but not nonparametric, as it involves a parameter $\theta$.