Abstract
Unfortunately many of the numerous algorithms for computing the cdf and noncentrality
parameter of the noncentral F and beta distributions can return completely incorrect results as
demonstrated in the paper by examples. Existing algorithms are scrutinized and those parts
that involve numerical difficulties are identified. As a result, a pseudo code is presented in
which all the known numerical problems are resolved. This pseudo code can be easily
implemented in programming language C or FORTRAN without understanding the
complicated mathematical background.
Symbolic evaluation of a finite and closed formula is proposed to compute exact cdf values.
This approach makes it possible to check quickly and reliably the values returned by
professional statistical packages over an extraordinarily wide parameter range without any
programming knowledge.
This research was motivated by the fact that a most useful table for calculating the size of
detectable effects for ANOVA tables contains suspicious values in the region of large
noncentrality parameter values compared to the values obtained by Patnaik's 2-moment
central-F approximation. The reason is identified and the corrected form of the table for
ANOVA purposes is given. The accuracy of the approximations to the noncentral-F
distribution is also discussed.
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