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).
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.
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].
- 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.
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.
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).
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:
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++).