# Two sample Kolmogorov-Smirnov test

`test-ks2Test.Rd`

Tests if two series are distributionally equivalent using two sample Kolmogorov-Smirnov test.

## Arguments

- x, y
numeric vectors of data values.

- title
an optional title string, if not specified the inputs data name is deparsed.

- description
optional description string, or a vector of character strings.

## Details

The test `ks2Test`

performs a Kolmogorov-Smirnov two sample
test that the two data samples, `x`

and `y`

, come from the
same distribution, not necessarily a normal distribution. That means
that it is not specified what that common distribution is.

`ks2Test`

calls several times base R's `ks.test`

p-values for all three alternatives (two-sided, less, and greater),
as well as the exact p-value for the two-sided case.

Note that the p-values are computed under a hypothesis of i.i.d., which is rarely the case for time series. So, the results should be interpreted cautiosly if that is the case. The same applies when the data are residuals from fitted models.

## Value

an object from class `fHTEST`

## References

Conover, W. J. (1971);
*Practical nonparametric statistics*,
New York: John Wiley & Sons.

Lehmann E.L. (1986);
*Testing Statistical Hypotheses*,
John Wiley and Sons, New York.

## Examples

```
set.seed(1234)
## rnorm -
# Generate Series:
x = rnorm(50)
y = rnorm(50)
## ks2Test -
ks2Test(x, y)
#>
#> Title:
#> Kolmogorov-Smirnov Two Sample Test
#>
#> Test Results:
#> STATISTIC:
#> D | Two Sided: 0.24
#> D^- | Less: 0.24
#> D^+ | Greater: 0
#> P VALUE:
#> Alternative Two-Sided: 0.1124
#> Alternative Exact Two-Sided: 0.1124
#> Alternative Less: 0.0562
#> Alternative Greater: 1
#>
```