Computing the Non-Central Beta Distribution Function

Chattamvelli, Rajan; Shanmugam, F.

doi:10.1111/1467-9876.00055

Cited by 10 publications

(12 citation statements)

References 10 publications

(11 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In order to avoid the under/overflow problems caused by starting the summation always at 0 = i several authors suggest [Guirguis (1990), Posten (1993), Chattamvelli and Shanmugam (1997), Benton and Krishnamoorthy (2003)] starting from an index approximately equal to 2 / λ and then work outward (increasing and decreasing i). Note that cancellation may occur whenever (5) is used in the forward iteration set.…”

Section: Round-off Errormentioning

confidence: 99%

See 1 more Smart Citation

On the computation of the noncentral F and noncentral beta distribution

Baharev

Kemény

2008

Stat Comput

View full text Add to dashboard Cite

); and Sándor Kemény is professor at the same institution (email: kemeny@mail.bme.hu ). The authors wish to thank Mr. Richárd Király for his preliminary work. The authors are grateful to the Associate Editor of STCO and the unknown reviewers for their helpful suggestions. 2 ABSTRACT AND KEY WORDSUnfortunately 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.

show abstract

Section: Round-off Errormentioning

confidence: 99%

“…488-495. Subsequent computer programs were also published: Chattamvelli and Shanmugam (1997), Ding (1997), Tiwari and Yang (1997). Major modern statistical software packages offer this type of calculations.…”

Section: Introductionmentioning

confidence: 99%

On the computation of the noncentral F and noncentral beta distribution

Baharev

Kemény

2008

Stat Comput

View full text Add to dashboard Cite

show abstract

“…The number of correct significant digits is given in parentheses algorithm of Chattamvelli and Shanmugam (1997) is actually slightly less accurate than Frick's algorithm (Frick 1990) for those large values of λ that are shown in Table 5. Since the precise details of the computations are not given in Chattamvelli and Shanmugam (1997), we cannot tell where the algorithm in Chattamvelli and Shanmugam (1997) suffers from a loss of precision.…”

Section: Example 2: Comparing the Accuracy Of Numerical Algorithmsmentioning

confidence: 99%

“…One of the goals of Table 1 of Chattamvelli and Shanmugam (1997) was to illustrate that their algorithm gives more accurate results than Frick's algorithm (Frick 1990) for large values of λ. We reproduced selected rows of their table in Table 5, and extended it with an extra column showing the correct values up to 7 significant digits.…”

Section: Example 2: Comparing the Accuracy Of Numerical Algorithmsmentioning

confidence: 99%

“…Probability of the type I and type II errors are 0.05 and 0.10 respectively All given digits are verified with the last digit rounded to the nearest Except the last column, the values are taken from Table 1 of Chattamvelli and Shanmugam (1997); the last column with the correct values is computed with the proposed method. The number of correct significant digits is given in parentheses algorithm of Chattamvelli and Shanmugam (1997) is actually slightly less accurate than Frick's algorithm (Frick 1990) for those large values of λ that are shown in Table 5.…”

Section: Example 2: Comparing the Accuracy Of Numerical Algorithmsmentioning

confidence: 99%

See 1 more Smart Citation

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

2016

View full text Add to dashboard Cite

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 crosschecked, 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.

show abstract

Descriptive Statistics

Chattamvelli

Shanmugam

2023

Synthesis Lectures on Mathematics &Amp; Statistics

View full text Add to dashboard Cite

Computing the Non-Central Beta Distribution Function

Cited by 10 publications

References 10 publications

On the computation of the noncentral F and noncentral beta distribution

On the computation of the noncentral F and noncentral beta distribution

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

Descriptive Statistics

Contact Info

Product

Resources

About