A Family of Near-Exact Distributions Based on Truncations of the Exact Distribution for the Generalized Wilks Lambda Statistic

Grilo, Luís M.; Coelho, Carlos A.

doi:10.1080/03610926.2011.604146

Cited by 4 publications

(1 citation statement)

References 8 publications

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“…where χ 2 pq represents the chi-square distribution with pq degrees of freedom, or by using other known approximations, see e.g. [23,24,25,26,27].…”

Section: Characteritic Function Of the Wilks's Test Statisticmentioning

confidence: 99%

Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function

Witkovský

2019

Journal of Applied Statistics

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Application of the exact statistical inference frequently leads to a non-standard probability distributions of the considered estimators or test statistics. The exact distributions of many estimators and test statistics can be specified by their characteristic functions. Typically, distribution of many estimators and test statistics can be structurally expressed as a linear combination or product of independent random variables with known distributions and characteristic functions, as is the case for many standard multivariate test criteria. The characteristic function represents complete characterization of the distribution of the random variable. However, analytical inversion of the characteristic function, if possible, frequently leads to a complicated and computationally rather strange expressions for the corresponding distribution function (CDF/PDF) and the required quantiles. As an efficient alternative, here we advocate to use the well-known method based on numerical inversion of the characteristic functions -a method which is, however, ignored in popular statistical software packages. The applicability of the approach is illustrated by computing the exact distribution of the Bartlett's test statistic for testing homogeneity of variances in several normal populations and the Wilks's Λ-distribution used in multivariate hypothesis testing.

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“…where χ 2 pq represents the chi-square distribution with pq degrees of freedom, or by using other known approximations, see e.g. [23,24,25,26,27].…”

Section: Characteritic Function Of the Wilks's Test Statisticmentioning

confidence: 99%

Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function

Witkovský

2019

Journal of Applied Statistics

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Approximate Finite Forms for the Cases Not Covered by the Finite Representation Approach

Coelho

Arnold

2019

Finite Form Representations for Meijer G and Fox H Functions

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The Exact and Near-Exact Distributions for the Statistic Used to Test the Reality of Covariance Matrix in a Complex Normal Distribution

Grilo

Coelho

2017

Springer Proceedings in Mathematics &Amp; Statistics

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A Family of Near-Exact Distributions Based on Truncations of the Exact Distribution for the Generalized Wilks Lambda Statistic

Cited by 4 publications

References 8 publications

Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function

Computing the exact distribution of the Bartlett's test statistic by numerical inversion of its characteristic function

Approximate Finite Forms for the Cases Not Covered by the Finite Representation Approach

The Exact and Near-Exact Distributions for the Statistic Used to Test the Reality of Covariance Matrix in a Complex Normal Distribution

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