Testing a distribution with the Kolmogorov-Smirnov distribution: kolmogorovt

### 7.5.5 Testing a distribution with the Kolmogorov-Smirnov distribution: kolmogorovt

The kolmogorovt command will use the Kolmogorov test to compare sample data to a specified continuous distribution. You need to provide kolmogorovt with either two lists of data or a list of data followed by the name of a distribution with the parameters. The kolmogorovt command will return three values:

- The D statistic, which is the maximum distance between the cumulative distribution functions of the samples or the sample and the given distribution.
- The K value, where K = D√n (for a single data set, where n is the size of the data set) or K=D√n1 n2 /(n1 + n2) (when there are two data sets, with sizes n1 and n2). The K value will tend towards the Kolmogorov-Smirnov distribution as the size of the data set goes to infinity.
- 1 - kolmogorovd(K), which will be close to 1 when the distributions look like they match.

For example, if you enter

kolmogorovt(randvector(100,normald,0,1),normald(0,1))

you might get

["D=",0.112592987625,"K=",1.12592987625,"1-kolmogorovd(K)=",0.158375510292]

and if you enter

kolmogorovt(randvector(100,normald,0,1),student(2))

you might get

["D=",0.0996114067923,"K=",0.996114067923,"1-kolmogorovd(K)=",0.27418851907]