kolmogorov-stephens-test

Simple C code for applying Kolmogorov test and test Stephens result

Compiling the code

Compilation for Linux

To compile the code just run make in the project dir.

make

After compilation 3 executables will be generated: deviation_statistics, simulate_data and stephens

Compilation for Window

Download the MinGW compiler: 'http://sourceforge.net/projects/mingw-w64/files/Toolchains%20targetting%20Win32/Personal%20Builds/mingw-builds/installer/mingw-w64-install.exe/download' In MinGW terminal and run the command:

mingw32-make

After compilation 3 executables will be generated: deviation_statistics.exe, simulate_data.exe and stephens.exe

Running the code

This project contains 3 executalbe programs each of them will be described in the next chapter

Program simulate_data

This program is used to generate set of random variables.

Usage:

./simulate_data <type> <file_name> <number_of_points>
     <type> - currently supported - are gauss or pseudo gauss.
     <file_name> - output file name
    <number_of_points> - the number of the generated points

Example for Linux:

./simulate_data gauss test_1000.txt 1000

Example for Windows:

simulate_data.exe gauss test_1000.txt 1000

This example will produce file test_1000.txt witl the following content:

$ head -n 5 test_1000.txt 
#1000
0.693775
2.050064
-0.022952
-0.934158
$

Program stephens

M. A. Stephens, "EDF Statistics for Goodness of Fit and Some Comparisons" J. of Amer. Statist. Assoc., 69, 730-737 (1974). http://www.math.utah.edu/~morris/Courses/6010/p1/writeup/ks.pdf Empirical Distribution Function EDF F[i]. Reject hypothesis at chosen level of significance. (double) sqN= sqrt(n) - .01 + .85/sqrt(n); Probability{max [sqNfabs(F-F^)]>D}=alpha Table 1, 1.3 Modification, mu and sigma unknown. D_alpha refers to upper tail critical value of the Kolmogorov-Smirnov statistics at level alpha, giving a (1-alpha) confidential interval.

alpha D

15% 0.775 10% 0.819 5% 0.895 2.5% 0,995 1.0% 1.035

Usage:

./stephens <file_name>

Example for Linux:

./stephens test_1000.txt

Example for Windows:

stephens.exe test_1000.txt

The first line of the input file should contain the number of random variables in the file. Like:

$ head -n 5 test_1000.txt 
#1000
0.693775
2.050064
-0.022952
-0.934158
$

Program deviation_statistics

This program is used to calculate sqrt(N)*D_N as function of N

Example for Linux

./deviation_statistics test 1000000

Example for Windows

deviation_statistics.exe test 1000000