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

The computations involving the noncentral-F distribution are notoriously difficult to implement properly in floating-point arithmetic: Catastrophic loss of precision, floating-point underflow and overflow, drastically increasing computation time and program hang-ups, and instability due to numerical...

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Detalles Bibliográficos
Autores principales: Baharev, Ali, Schichl, Hermann, Rév, Endre
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer Berlin Heidelberg 2016
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7010373/
https://www.ncbi.nlm.nih.gov/pubmed/32103863
http://dx.doi.org/10.1007/s00180-016-0701-3
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author Baharev, Ali
Schichl, Hermann
Rév, Endre
author_facet Baharev, Ali
Schichl, Hermann
Rév, Endre
author_sort Baharev, Ali
collection PubMed
description The computations involving the noncentral-F distribution are notoriously difficult to implement properly in floating-point arithmetic: Catastrophic loss of precision, floating-point underflow and overflow, drastically increasing computation time and program hang-ups, and instability due to numerical cancellation have all been reported. It is therefore recommended that existing statistical packages are cross-checked, and the present paper proposes a numerical algorithm precisely for this purpose. To the best of our knowledge, the proposed method is the first method that can compute the noncentrality parameter of the noncentral-F distribution with guaranteed accuracy over a wide parameter range that spans the range relevant for practical applications. Although the proposed method is limited to cases where the the degree of freedom of the denominator of the F test statistic is even, it does not affect its usefulness significantly: All of those algorithmic failures and inaccuracies that we can still reproduce today could have been prevented by simply cross-checking against the proposed method. Two numerical examples are presented where the intermediate computations went wrong silently, but the final result of the computations seemed nevertheless plausible, and eventually erroneous results were published. Cross-checking against the proposed method would have caught the numerical errors in both cases. The source code of the algorithm is available on GitHub, together with self-contained command-line executables. These executables can read the data to be cross-checked from plain text files, making it easy to cross-check any statistical software in an automated fashion.
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spelling pubmed-70103732020-02-24 Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy Baharev, Ali Schichl, Hermann Rév, Endre Comput Stat Original Paper The computations involving the noncentral-F distribution are notoriously difficult to implement properly in floating-point arithmetic: Catastrophic loss of precision, floating-point underflow and overflow, drastically increasing computation time and program hang-ups, and instability due to numerical cancellation have all been reported. It is therefore recommended that existing statistical packages are cross-checked, and the present paper proposes a numerical algorithm precisely for this purpose. To the best of our knowledge, the proposed method is the first method that can compute the noncentrality parameter of the noncentral-F distribution with guaranteed accuracy over a wide parameter range that spans the range relevant for practical applications. Although the proposed method is limited to cases where the the degree of freedom of the denominator of the F test statistic is even, it does not affect its usefulness significantly: All of those algorithmic failures and inaccuracies that we can still reproduce today could have been prevented by simply cross-checking against the proposed method. Two numerical examples are presented where the intermediate computations went wrong silently, but the final result of the computations seemed nevertheless plausible, and eventually erroneous results were published. Cross-checking against the proposed method would have caught the numerical errors in both cases. The source code of the algorithm is available on GitHub, together with self-contained command-line executables. These executables can read the data to be cross-checked from plain text files, making it easy to cross-check any statistical software in an automated fashion. Springer Berlin Heidelberg 2016-12-08 2017 /pmc/articles/PMC7010373/ /pubmed/32103863 http://dx.doi.org/10.1007/s00180-016-0701-3 Text en © The Author(s) 2016 Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
spellingShingle Original Paper
Baharev, Ali
Schichl, Hermann
Rév, Endre
Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy
title Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy
title_full Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy
title_fullStr Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy
title_full_unstemmed Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy
title_short Computing the noncentral-F distribution and the power of the F-test with guaranteed accuracy
title_sort computing the noncentral-f distribution and the power of the f-test with guaranteed accuracy
topic Original Paper
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC7010373/
https://www.ncbi.nlm.nih.gov/pubmed/32103863
http://dx.doi.org/10.1007/s00180-016-0701-3
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