Table of maximum likelihood estimates for the bingham distribution

Mardia, Kanti V.; Zemroch, P. J.

doi:10.1080/00949657708810165

Cited by 23 publications

(19 citation statements)

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“…As can be seen, (10) alone provides a useful estimate of k 2 ; within a few per cent, when Fl < 0.02, for k2 up to about -1 (F2 -0.36). Moreover, the change of k z for increasing t l (Mardia & Zemroch 1977) suggests that interpolation is adequately accurate for routine applications.…”

Section: Numerical Results and Conclusionmentioning

confidence: 99%

“…We now verify this by showing that equation (3) for k z indeed reduces to (10) as k l -+ -m. Following Mardia & Zemroch (1977), we rewrite (3) as : (1 8) asymptotically as x -+ (e.g. Abramowitz & Stegun 1965, p. 377).…”

Section: Relation To the 3-d Casementioning

confidence: 99%

“…For routine work, however, a need for extensive computation is obviated by tabulating k l and k2 as functions of the normalized eigenvalues and F2 and interpolating. Mardia & Zemroch (1977), for example, list kl and k2 for the normalized eigenvalues at intervals of 0.02.…”

Section: Introductionmentioning

confidence: 99%

“…However, Mardia & Zemroch (1977) do not tabulate values for tl <0.02, where lkll becomes large. Moreover, although they note that large Ikl I and Ik2 I can be estimated from the asymptotic relation (Bingham 1974):…”

Section: Introductionmentioning

confidence: 99%

“…The values for ?, = 0 are calculated from the limiting relation 2i, -1 = I , (%k2)/I0 (%k,) (see text); other values were calculated by numerical integration(Onstott 1980), and checked against the values ofMardia & Zemroch (1977) …”

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confidence: 99%

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Estimation of the Bingham distribution function on nearly two-dimensional data sets

Gillett¹

1986

Geophysical Journal International

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In cases where directional data, such as palaeomagnetic directions, lie nearly along a great circle, a good approximation to the maximum likelihood estimate of the intermediate concentration parameter kz in the Bingham probability distribution is given by:where tz is the intermediate eigenvalue, N is the number of samples, and the Zi are the appropriate modified Bessel functions of the first kind. This estimate, the asymptotic limit as the smallest eigenvalue t l +O, corresponds to restricting all points to lie on a great circle. The limit is also useful as an endpoint for interpolation, especially since numerical calculation in this region is difficult.

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Section: Numerical Results and Conclusionmentioning

confidence: 99%

Section: Relation To the 3-d Casementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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