%0 Journal Article %1 noauthororeditor %A Bahaarev, Ali %A Kémeny, Sándor %D 2008 %J Statistics and Computing %K distributions noncentral statistics %N 3 %P 333-340 %T On the Computation of the noncentral F and noncentral beta distribution %U http://reliablecomputing.eu/ncbeta.pdf %V 18 %X 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.

@article{noauthororeditor, 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. }, added-at = {2015-02-25T00:34:22.000+0100}, author = {Bahaarev, Ali and K\'{e}meny, S\'{a}ndor}, biburl = {https://www.bibsonomy.org/bibtex/247ab4d5ef3b4e0acad396b17a8aa00ad/shabbychef}, interhash = {0beb7f674f9daa747ca3fd1561442fd1}, intrahash = {47ab4d5ef3b4e0acad396b17a8aa00ad}, journal = {Statistics and Computing}, keywords = {distributions noncentral statistics}, number = 3, pages = {333-340}, timestamp = {2015-02-25T00:34:22.000+0100}, title = {On the Computation of the noncentral F and noncentral beta distribution}, url = {http://reliablecomputing.eu/ncbeta.pdf}, volume = 18, year = 2008 }