Skip to content
This repository has been archived by the owner on Nov 9, 2018. It is now read-only.
/ mindiffver Public archive

Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy

License

Notifications You must be signed in to change notification settings

baharev/mindiffver

Folders and files

NameName
Last commit message
Last commit date

Latest commit

 

History

8 Commits
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 

Repository files navigation

Reproducing the numerical results of the paper

The algorithm is described in the academic paper Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy. To reproduce the numerical results of this paper on Linux run:

mindiffver  <input.txt  >output.txt

or on Windows:

mindiffver.exe  <input.txt  >output.txt

The corresponding executables and the input.txt file are in the binary_distribution directory. The executables should work on any i386 compatible architecture. The downside is that they are roughly 7x slower than an executable optimized specifically for your CPU.

The only relevant source file is the main.cpp file. The other source files belong to the third party interval arithmetic library C-XSC (see the paper).

Example

This program reads from the standard input, and writes to the standard output, line-by-line. If you have a table of the data to verify in a text file called input.txt, then you can run this program like this:

mindiffver  <input.txt  >output.txt

or on Windows:

mindiffver.exe  <input.txt  >output.txt

The verified results will be written to the output.txt file.

The format of the input.txt and output.txt are detailed right below.

Input format

Each line of the input is supposed to have the following format:

a  b  x_0  lambda_0  alpha  beta  eps_x  eps_lambda

where the items are separated by arbitrary whitespace, a and b are the shape parameters of the noncentral beta distribution, x_0 is the upper alpha quantile of the (central) beta distribution, beta is the Type II error beta (not detecting an effect; power=1-beta), eps_x and eps_lambda are the inflation parameters. The search intervals for the correct value of x and lambda are:

x = [(1-eps_x)*x_0, (1+eps_x)*x_0], and
lambda = [(1-eps_lambda)*lambda_0, (1+eps_lambda)*lambda_0]. 

Ranges (checked by the program)

  • All input values must be strictly positive
  • b must be integer
  • x, alpha, beta, eps_x, eps_lambda < 1 must hold
  • eps_x >= tol_x, and eps_lambda >= tol_lambda must hold, where tol_x = 10^-12 and tol_lambda = 10^-10 are the currently set tolerances for x and lambda in the interval Newton iteration.

Assumptions (not checked)

The parameters are assumed to lie in the domain that is relevant for practical applications, roughly: a <= 25, b <= 500, 0.01 <= alpha, beta <= 0.99; the inflation parameters are also assumed to be sane, say < 10^-4. Violating these assumptions may cause performance degradation and the algorithm may start reporting failures but incorrect results will never be produced.

Output format

There are 3 possible outcomes:

a) If the input line contains a solution and the interval Newton method is successful in verifying it, then the output is a line matching the format of the input line (items are guaranteed to be tab separated) where x and lambda are guaranteed to have the precision given in the last two columns (currently set to 10^-12 and 10^-10 relative error, respectively).

b) If the input line does NOT contain a solution and the interval Newton method is successful in verifying it, then the output is a single line saying: "The search interval [...] is verified NOT to contain a zero".

c) In all other cases a single line error message starting with "Failed ..." is printed. See the failures.txt input file that systematically triggers all known failure modes, except for the first and the last line of that file (those two lines must succeed).

Compiling from source

You may consider using the binary distribution in which case you avoid the hassle of compiling the software. In order to install it from source, install C-XSC:

http://www.xsc.de/

with the default settings, except that both dynamic and static libraries are built. Make sure that all the unit tests of C-XSC pass! The unit tests are automatically executed as part of the installation procedure. If you have difficulties passing the unit tests, try setting the rounding mode to soft.

Then, in the directory where the source files of the software are, issue the following command:

g++ -O3 -I/path/to/cxsc/include -L/path/to/cxsc/lib *.cpp -Wl,--static -lcxsc -Wl,-Bdynamic -o mindiffver

where the paths /path/to/cxsc/include and /path/to/cxsc/lib are set according to your C-XSC installation path. This command assumes that you have gcc (g++).

About

Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy

Topics

Resources

License

Stars

Watchers

Forks

Releases

No releases published

Packages

No packages published

Languages